text:
\section{Introduction}
\label{sec:intro}

Beam damage to the specimen is one of the most fundamental limits to the data quality in electron microscopy. In biological applications the acceptable dose is often below ten electrons per square \aa ngstr\"om, no matter if one images biological macromolecules  \cite{henderson1995,rez2003,baker2010} or records diffraction patterns of protein crystals  \cite{shi2013}. Although not as severe, beam sensitivity is an issue in materials science as well and researchers go to great lengths to limit it \cite{egerton2004,kaiser2011,jiang2012,egerton2015}. Furthermore, with the increased occurrence of soft and hard matter being interfaced into so-called hybrid materials  \cite{kirmse2016} biology's low upper bound for the electron dose now encroaches on the realm of materials physics too. A current trend in scanning transmission electron microscopy (STEM) seeks to limit electron exposure of the specimen by invoking compressed sensing \cite{romberg2008} (CS) in the recording process  \cite{stevens2014,beche2016,reed2017,donati2017}.

For applications with photon radiation, dose limitation is often a driving factor as well, for example when using potentially hazardous X-rays for computed tomography \cite{kubo2008}. Furthermore, limiting the recording time can be a valid goal in itself.

In CS, the signal $x$ is retrieved from the recordings $y$ that have been produced by the sensing matrix $A$ operating on $x$, i.e. $y = A x$. Recovery of $x$ from a surprisingly low number of measurements $y$ is possible if these measurements are incoherent  \cite{candes2007} to the signal and a sparsity constraint can be imposed. In general that involves expressing $x$ in a mathematical basis where it is sparse, for instance many photographs are sparse in a wavelet basis. For piecewise linear signals such an explicit decomposition can be omitted and $x$ can be retrieved instead by expressing that its total generalized variation (\ensuremath{\text{TGV}}) must be minimal; this approach is known as TV minimization \cite{candes2006}.

In order to make the measurements incoherent to the signal, sensing matrices conventionally have zero-mean independent and identically distributed (iid) random variables for entries. In the analysis of the respective error bounds, noise is often not considered, or assumed additive and/or bounded.

\subsection{Contribution of this paper}

In this paper it is acknowledged that in many experiments the total dose on the specimen is of greater importance than the number of measurements, and hence the performance of various CS set-ups is assessed under the constraint of constant total illumination. In other words, we investigate how to optimally make use of a given electron or photon budget.

Two fundamentally different and common set-ups are analyzed: the single-pixel set-up and annular dark field STEM (ADF-STEM).  These two instances respectively represent experiments where the illumination is caused by external sources outside of the scientist's control and those where they are in full command of the irradiation, between them covering most practical situations.

The Fisher information that the measurements contain about the underlying parameters is evaluated through the A-optimality information criterion ($\ensuremath{\text{AOC}}$)  \cite{rao1945,cramer1946,lehmann2006,vandenbroek2009,vandenbroek2011}.  Furthermore, a heuristic quantity, the detective quantum efficiency (DQE), is developed.  With the aid of simulations it is shown that the $\ensuremath{\text{DQE}}$ tracks the $\ensuremath{\text{AOC}}$ well.  Furthermore, a novel regularization is introduced and through simulations and experiment it is empirically demonstrated that the associated reconstructions attain minimum mean squared error (MSE) at experimental settings predicted by the DQE as optimal.

Having established the $\ensuremath{\text{DQE}}$'s validity, its analytical tractability is used to show that for the investigated sensing matrices and in the absence of read-out noise, i.e. with only Poisson noise present, compressed sensing does not raise the amount of Fisher information in the recordings above that of a Shannon sampled signal.  This is reflected in the reconstruction results that yield a comparable MSE when both data sets are treated with the same algorithm to isolate the influence of the recording protocol.

Furthermore, the experimental designs are optimized, i.e. the fraction of on-pixels for best reconstruction quality is given as a function of particle dose, read-out noise and other experimental parameters.

\subsection{Relation to previous work}

The conventional zero-mean sensing matrices in, for instance, \cite{candes2006,candes2007} are not physically realizable for the particle-counting experiments investigated in this paper: the single-pixel camera and ADF-STEM. In a pivotal paper, Raginsky  \cite{raginsky2010} et al. have shown that in that context the use of a sensing matrix that preserves non-negativity and flux combined with the non-additive and dose dependent unbounded Poisson noise, has such a large and adverse effect on the derived error bounds that they do not even approach the conventional bounds in the limit of high dose and the associated relatively low noise.

CS has been analyzed from the perspective of Fisher information and the $\ensuremath{\text{AOC}}$ before \cite{babadi2009,miller2009,niazadeh2012,nielsen2012,pakrooh2013,pakrooh2016}.  These works, however, did not consider sensing matrices that preserve non-negativity and flux or the non-additive and dose dependent unbounded Poisson noise.  That doing so yields qualitatively different results is illustrated by the fact that the finding in \cite{nielsen2012} that ``the estimation accuracy [degrades] by at least the down-sample factor'' is reproduced in this work when just read-out noise is considered, but not when only Poisson noise is taken into account.

\subsection{Organization of the paper}

This paper is organized as follows. The image formation of ADF-STEM and the single-pixel camera is treated in Sec. \ref{sec:imafor}; the basics of compressed sensing pertaining to our problem are dealt with in Sec. \ref{sec:comsen}; in Sec. \ref{sec:staexp} Fisher information and the A-optimality information criterion are explained and the application of statistical experimental design to the compressed sensing set-ups is developed; the results are reported and discussed in Secs. \ref{sec:resdis} and \ref{sec:dis}; and in Sec. \ref{sec:con} the conclusions are drawn.

\section{Image formation}
\label{sec:imafor}

In this section the image formation for the single-pixel camera and ADF-STEM is established.

\subsection{Single-pixel camera}
\label{sec:sinpix}

A way of realizing a single-pixel camera \cite{duarte2008} is by projecting an image onto an array of switchable mirrors located in the image plane of an objective lens whose conjugate plane contains a photon detector on the optical axis; see Fig. \ref{fig:expsetup} for a sketch of the setup. Each of the mirrors in the array can be switched on or off, and fractional on-values can be obtained by tuning the pixels' on-time.

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{ExperimentalSetups.jpg}
  \caption{\label{fig:expsetup} \emph{(a)}: In the single-pixel camera the scene is projected onto an array of switchable mirrors, and the reflected light is focused onto the single-pixel detector. (Sketch after  \cite{baraniuk2007}) \emph{(b)}: In ADF-STEM an electron probe is scanned over the object, and electrons scattered to higher angles are integrated in an annular detector in the far-field.}
\end{figure}

The linear image formation model is given as
\begin{eqnarray}
\label{eq:linimafor}
  \ensuremath{\text{E}}(y) = I A x,
\end{eqnarray}
where the measurement vector $y$ has $M$ elements, the two-dimensional object is written in long-vector format as $x$ and has $N$ elements, the sensing matrix $A$ has dimensions $M \times N$ and $I \mu$ is the average number of photons reflecting off each of the object's pixels, with $\mu$ the average of $x$ and $\ensuremath{\text{E}}$ denoting the expectation value.  Although not treated explicitly in this work, it is worthwhile noting that $I$ depends on $N$ through $I \propto 1 / N$, thus expressing that a finite number of photons must be budgeted over the $N$ pixels.

Two distinct choices for $A$ are investigated in this paper:
\begin{enumerate}
 \item[] \textbf{PIX$_{\text{Di}}$}: each mirror in the array has a chance $p$ to provide the discrete value $v$ of $1$ (``on'') and a chance $1-p$ to provide $0$ (``off'');
 \item[] \textbf{PIX$_{\text{Fr}}$}: each mirror has a chance $p$ to provide a fractional value $v$ drawn from a uniform distribution on $[0,1]$, and a chance $1-p$ to provide $0$.
\end{enumerate}
This approach allows the value for $p$ to be optimized. Since the single-pixel camera is to be evaluated for a constant recording time, the elements of $A$ corresponding to on-pixels are set to $v/M$ and those corresponding to off-pixels to $0$, expressing that a constant expected total number of photons $NI\mu$ is reflecting off the object. Note that although the number of photons impinging on the sample is constant, the recorded number of photons scales with $p$.

The pixel-by-pixel raster scan, or Shannon sampling, is obtained with sensing matrix PIX$_{\text{Di}}$ \ when $p$ is set to $1/N$ and the matrix $A$ is diagonal with $M = N$. The subsequent reconstruction of the image under the application of a sparsity constraint then comes down to denoising.

The case of Gaussian distributed values in the sensing matrix is not considered in this paper.  It is trivial to adapt the conventional zero-mean binary and uniformly distributed values to the non-negative distributions considered here: shifting the distributions' mean accomplishes this without introducing distortions to the distributions.  A mere translation is not sufficient for the Gaussian distribution however, its non-boundedness implies additional clipping of remaining negative values \emph{and} too-high positive values.  The latter is necessary because a finite recording time sets an upper limit on the value of an on-pixel.  The analysis needed to separate the influence of such a distortion from the influence of the mere non-negativity falls outside of the scope of this work.

\subsection{ADF-STEM}
\label{sec:adfste}

For ADF-STEM the electron beam is condensed onto the specimen and scanned across it. For each beam position an annular detector in the far-field integrates the electrons scattered to its surface; see Fig. \ref{fig:expsetup}. Although analyzing  the resulting gray values in terms of the specimen's chemical composition \cite{hartel1996} is important, it is not the subject of this work and is hence not treated or attempted. Instead the signal $x$ is taken as the expected detector output for a certain beam position.

The image formation model is again given by (\ref{eq:linimafor}), and these choices of $A$ are investigated:
\begin{enumerate}
  \item[] \textbf{ADF$_{\text{CS}}$}: $A$'s elements are switched on with a probability $p$ and given a value of $1/(pN)$, off-pixels are set to $0$;
  \item[] \textbf{ADF$_{\text{Sh}}$}: $A$ is $N \times N$ with only the diagonal elements non-zero and equal to $M/N$.
\end{enumerate}
These two matrices allow comparison under equal dose in the recordings since they yield an expected total dose in $y$ of $MI\mu$, corresponding to an average of $I\mu$ and $IM\mu / N$ per individual measurement for sensing matrices ADF$_{\text{CS}}$ \ and ADF$_{\text{Sh}}$, respectively.

Note that in ADF-STEM the operator has direct control over the delivered dose through the beam intensity, dwell time and beam-blanking at will so that all electrons that scatter from the object and that could in principle be detected, actually are detected and contribute to the signal $y$; this recording mode is fundamentally different from the single-pixel case.

Sensing matrix ADF$_{\text{CS}}$ \ is analogous to the single-pixel set-up and can be experimentally realized through fast beam deflection as detailed in  \cite{beche2016,reed2017}; matrix ADF$_{\text{Sh}}$ \ represents a classic raster scan, or Shannon scan, with a total intensity matched to the CS case.  A special case of ADF$_{\text{CS}}$ \ is obtained by equating $p$ to $1/N$ and corresponds to sampling the specimen in $M$ randomly selected points.  This is known as inpainting \cite{papafitsoros2014} and its treatment here is motivated by the interest it currently receives from various research groups \cite{stevens2014,beche2016}.

\subsection{Noise models}
\label{sec:noimod}

Since both imaging techniques are essentially particle counting experiments (photons or electrons) the measurements $y_i$ follow a Poisson probability density distribution
\begin{eqnarray}
\label{eq:poidis}
  \frac{ \(I A_i x\)^{y_i} }{ y_i! } \exp\( -I A_i x \)
\end{eqnarray}
with $A_i$ the $i^{\text{th}}$ row of $A$. This Poisson distribution has mean and variance $I A_i x$.

In the case the recording device is not perfect it could add read-out noise. To keep the problem analytically tractable the Poisson distribution is approximated with a normal distribution with mean and variance $I A_i x$, and the read-out noise is modeled as normal additive noise with zero mean and variance $c$. Since both contributions are independent their variances add, yielding
\begin{eqnarray}
\label{eq:nordis}
  \frac{1}{\sqrt{ 2 \pi \( I A_i x + c \) }} \exp\( \frac{-\(y_i - I A_i x\)^2}{2\( I A_i x + c \)} \)
\end{eqnarray}
as distribution for $y_i$.

The approximation of a Poisson distribution as a Gaussian is of great practical value in the theoretical analysis but needs some justification. In practice, the actual noise properties are rarely truly Poisson; the Poisson distribution is itself an approximation to the real system, and this provides some latitude to choose a more mathematically convenient approximate model.

For example, in ADF-STEM, the detection is indirect such that the signal produced by each electron is a random variable, and the aggregated signal yields a probability distribution that scales as Poisson but is not actually Poisson for several reasons. First, the distribution is continuous, not discrete. Second, the constant of proportionality between the signal and the variance is in general not unity. The effect of this calibration factor on the results in this article is nothing more than a trivial rescaling factor. Third, the readout noise also contributes, especially at low signal levels where it can be dominant. Thus, in the very regime where the Poisson distribution is most poorly approximated by a Gaussian, the dominant noise contribution is in fact Gaussian.

Since much of CS literature considers read-out noise only it is investigated in this paper too. The noise is assumed normal and additive with zero mean and variance $c$, so that $y_i$ is drawn from the distribution
\begin{eqnarray}
\label{eq:rdtdis}
  \frac{1}{\sqrt{ 2 \pi c }} \exp\( \frac{-\(y_i - I A_i x\)^2}{2 c } \).
\end{eqnarray}

\section{Compressed sensing}
\label{sec:comsen}

In compressed sensing (CS) under-determined or ill-posed problems are alleviated by regularization of the solution. In general a basis is defined in which the solution is expected to be sparse, and regularizing then means finding that solution with minimal $\ell_1$-norm in said basis.

An explicit decomposition can be avoided in the special case of piecewise linear objects $x$  with the aid of Hessian regularization \cite{scherzer1998,papafitsoros2014}.  To this end the total generalized variation ($\ensuremath{\text{TGV}}$) is defined as,
\begin{eqnarray}
\label{eq:tv}
  \ensuremath{\text{TGV}}(x) = \sum_k \ensuremath{\left|} s_k \ensuremath{\right|}, \text{ with } s = H x,
\end{eqnarray}
where $s_k$ is the Laplacian in $x_k$, calculated approximately by the operator $H$ which implements a convolution with the kernel
\begin{eqnarray}
 \begin{pmatrix}
  0& 1 & 0 \\
  1 & -4 & 1 \\
  0& 1 & 0
 \end{pmatrix}. \label{eq:lapKernel}
\end{eqnarray}
This approach is often used in inpainting \cite{papafitsoros2014}.

The signal $x$ can then be retrieved by solving the constraint optimization problem
\begin{eqnarray}
\label{eq:tvm}
  \min_x \ensuremath{\text{TGV}}(x) \ \text{ s.t. } \ IAx = y.
\end{eqnarray}
However, solving this system with exact compliance to the constraint leads to overfitting and a solution that cannot be considered very sparse anymore.  Instead, a constraint is stated that can be obeyed exactly without overfitting and can be complied with by minimizing an augmented Lagrangian \cite{nocedal1999} through an alternating direction scheme \cite{boyd2011,li2013,jiang2016}
\begin{eqnarray}
\label{eq:lnLElnL}
  \min_x \ensuremath{\text{TGV}}(x) \ \text{ s.t. } \ \ln L( y | x ) = \ensuremath{\text{E}} \(  \ln L( y | x ) \).
\end{eqnarray}
$\ln L$ is the log-likelihood of the measurements $y$ conditional on the model parameters $x$.  More details and the equivalence to a convex optimization problem are shown in App. \ref{sec:ElnL}.  The encouraging results and close correspondence of this choice of regularization to the behavior predicted by the DQE are presented in this paper as empirical results.\footnote{The MATLAB implementation of this algorithm, sparseElnL, is made freely available (\url{https://github.com/woutervandenbroek/sparseElnL}).}

Although not needed for solving (\ref{eq:lnLElnL}), an explicit transformation
\begin{eqnarray}
\label{eq:Gs}
  x = G s,
\end{eqnarray}
is necessary for our analysis, changing the image formation model from (\ref{eq:linimafor}) into
\begin{eqnarray}
\label{eq:I0AGs}
  \ensuremath{\text{E}}(y) = I A G s.
\end{eqnarray}

Since $s$ is computed through a convolution with kernel (\ref{eq:lapKernel}), the inverse operator $G$ can be obtained by transforming to Fourier space, inverting, zeroing the dc-component and transforming back to real space. As this resets the mean value to $0$, $s$ is extended by one element containing the mean, and the appropriate column is appended to $G$; similarly, a corresponding row is appended to $H$ as well.

\section{Statistical experimental design}
\label{sec:staexp}

In this section the Fisher information matrix, the A-optimality criterion ($\ensuremath{\text{AOC}}$) and the detective quantum efficiency (DQE) of the various measurement schemes are discussed.

\subsection{Fisher information matrix}
\label{sec:fiinma}

The Fisher information  \cite{frieden1998,lehmann2006} \ensuremath{\mathcal{I}} \ quantifies how much information the measurements $y$ contain about the unknown parameters $s$ that model it. In this section and in Sec. \ref{sec:crarao} the signal support is assumed known, i.e. only the non-zero elements of $s$ are retained. The Fisher information is defined as the negative expectation value of the curvature of the measurements' log-likelihood function $\ln L(y|s)$
\begin{eqnarray}
\label{eq:fiin}
  \ensuremath{\mathcal{I}}_{k,\ell}(s) = -\ensuremath{\text{E}} \[ \frac{\partial^2 \ln L( y|s )}{\partial s_k \partial s_{\ell}} \].
\end{eqnarray}
If the measurements $y_i$ are drawn from the independent distributions $p_i(y_i|s)$, then
\begin{eqnarray}
  L( y|s ) = \prod_i  p_i( y_i | s ).
\end{eqnarray}

For the problems at hand, the distributions $p_i$ are given by the noise distributions in (\ref{eq:poidis}), (\ref{eq:nordis}) and (\ref{eq:rdtdis}). Working out (\ref{eq:fiin}) while taking (\ref{eq:Gs}) into account yields
\begin{eqnarray}
\label{eq:fipoi}
  \ensuremath{\mathcal{I}}_{k,\ell}(s) = I \sum_i \frac{[AG]_{i,k} [AG]_{i,\ell}}{ [AG]_i s }
\end{eqnarray}
for the Poisson distribution in (\ref{eq:poidis}),
\begin{eqnarray}
\label{eq:finor}
\begin{split}
  \ensuremath{\mathcal{I}}_{k,\ell}(s) = & \ I \sum_i \frac{[AG]_{i,k} [AG]_{i,\ell}}{[AG]_i s + c/I} \bigg( 1 + \\
  \ & \frac{1}{2I\( [AG]_i s + c/I \)} \bigg)
\end{split}
\end{eqnarray}
for the case in (\ref{eq:nordis}) with Poisson and read-out noise, and
\begin{eqnarray}
\label{eq:firdt}
  \ensuremath{\mathcal{I}}_{k,\ell}(s) = \frac{I^2}{c} \sum_i [AG]_{i,k} [AG]_{i,\ell}
\end{eqnarray}
for read-out noise only, as described in (\ref{eq:rdtdis}).

In order to calculate $\ensuremath{\mathcal{I}}(s)$, all zero entries of $s$ are removed, as are the corresponding columns of $G$ and rows of $H$. It can be seen immediately from (\ref{eq:Gs}) that this does not affect the image formation.

\subsection{Information criterion}
\label{sec:crarao}

In statistical experimental design experiments are set up so as to maximize a measure of the information the recordings contain about the unknown parameters that model them.  This requires compression of the information matrix into a single number, a so-called information criterion, that then is optimized with respect to the experimental settings ($p$ in this paper).

For this work, the oft-used A-optimality is chosen.  It is the trace of the inverse of the information matrix, divided by the number of unknowns, $K$,
\begin{eqnarray}
\label{eq:crbtv}
  \ensuremath{\text{AOC}} = \ensuremath{\text{tr}} \( \ensuremath{\mathcal{I}}(s)^{-1} \) / K.
\end{eqnarray}
Although various choices are possible, in \cite{cornell2002} it is noted that ``[A] design that is optimal for a given model using one [...] criteri[on] is usually near-optimal for the same model with respect to [...] other criteria.''

A-optimality has the added advantage that in case of unbiased estimators it serves as the lower bound on the mean squared error.   It is possible to attain this instance of the so-called Cram\'er Rao lower bound \cite{rao1945,cramer1946,lehmann2006} in practice; most notably  by a maximum likelihood estimation from a sufficient number of measurements \cite{lehmann2006}.  Nevertheless, one must keep in mind that foremost $\ensuremath{\text{AOC}}$ is a statement about the information contained in the measurements, independent of any estimation algorithm.  In view of the fact that the regularized estimates produced in CS are generally biased, the interpretation as a lower bound on the mean squared error is only of secondary importance in this context.\footnote{The MATLAB implementation of these calculations, sparseAOC, is made freely available (\url{https://github.com/woutervandenbroek/sparseAOC}).}

\subsection{Detective quantum efficiency}
\label{sec:dqe}

Rigorous as the $\ensuremath{\text{AOC}}$ is, it lacks generality in this context as it must be calculated for a particular sparsifying basis, example object $x$ and realization of $A$. The latter problem can be countered by averaging over multiple realizations of $A$, although this exacerbates an already demanding computation. Furthermore, it requires knowledge of the signal support and no analytical relation between the imaging system's settings and the reconstruction quality $\ensuremath{\text{AOC}}$ is provided.

In order to gain insight, the detective quantum efficiencies (DQE) of the various CS setups are introduced.  While conventionally the DQE characterizes noise properties of imaging devices \cite{rose1946,niermann2012}, it is slightly generalized here in order to characterize the recording set-up as a whole,
\begin{eqnarray}
  \ensuremath{\text{DQE}} = \alpha \frac{\ensuremath{\text{SNR}_{\text{out}}}^2}{\ensuremath{\text{SNR}_{\text{in}}}^2}. \label{eq:dqe}
\end{eqnarray}
$\ensuremath{\text{SNR}_{\text{out}}}$ and $\ensuremath{\text{SNR}_{\text{in}}}$ are the signal-to-noise ratios of the recorded signal and the incoming signal, respectively.  The prefactor $\alpha$ reflects the different number of measurements in both cases, hence $\alpha = M/N$ for sensing matrices PIX$_{\text{Di}}$, PIX$_{\text{Fr}}$ \ and ADF$_{\text{CS}}$, and $\alpha = 1$ for sensing matrix ADF$_{\text{Sh}}$.  More details are provided in App. \ref{sec:derdqe}.

The SNR is defined as the ratio of the standard deviation of the signal to the standard deviation of the noise.  For $\ensuremath{\text{SNR}_{\text{out}}}$ this is calculated as the recorded signal $y$, while for $\ensuremath{\text{SNR}_{\text{in}}}$ we use the best possible hypothetical reference signal allowed by Poisson noise given the number of available particles.  In case of the single-pixel camera this constitutes the signal that would be obtained with an ideal detector in lieu of each of the mirrors in the image plane, while for ADF-STEM it means spreading out the available dose over all pixels in the image; the respective expressions are (\ref{eq:snrinsp}) and (\ref{eq:snrinADF}).

Since the DQE is calculated from $y$ instead of $s$ knowledge of the support does not come into play.  Although more heuristic than the $\ensuremath{\text{AOC}}$, the DQE is more general as $s$ enters its expression through the average $\mu$ of $x$ only, and is independent of the particular realization of $A$ and only depends on the variance of $A$'s elements.

The results are summarized in Table \ref{tab:dqes}, where the new variables
\begin{eqnarray}
  r = \frac{M}{N} \text{, } \gamma = \frac{c N}{I \mu} \text{ and } \gamma' = \frac{c}{I \mu}, \label{eq:varssipi}
\end{eqnarray}
have been used. $r$ is the reduction, and $\gamma$ and $\gamma'$ the normalized variances of the read-out noise.

Note how the last column of the first two rows of Table \ref{tab:dqes} reproduces the $N/M$ dependency of the $\ensuremath{\text{AOC}}$ presented in Eq. 21 in \cite{nielsen2012} for read-out noise without Poisson statistics.

\begin{table}
\renewcommand{\arraystretch}{1.5}
\caption{DQEs for Various Sensing Matrices and Noise Models. }
\label{tab:dqes}
\center
\begin{normalsize}
\begin{tabular}{c | c c c }
  \hline
	\hline
	{\footnotesize Sensing} & \multicolumn{3}{c}{{\footnotesize Noise model}}\\
  {\footnotesize matrix}  & {\footnotesize Poisson} & {\footnotesize Poisson + read-out} & {\footnotesize read-out} \\
  \hline
   {\footnotesize PIX$_{\text{Di}}$}  & $\frac{1-p}{N}$ & $\frac{p(1-p)}{pN + r\gamma}$ & $\frac{p(1-p)}{r \gamma}$ \\
   {\footnotesize PIX$_{\text{Fr}}$}  & $\frac{2/3 - p/2}{N}$ & $\frac{p(1/3-p/4)}{pN/2 + r\gamma}$ & $\frac{p(1/3-p/4)}{r\gamma}$ \\
   {\footnotesize ADF$_{\text{CS}}$}  & $\frac{1-p}{pN}$ & $\frac{1-p}{pN}\frac{1}{1 + \gamma'}$ & $\frac{1-p}{pN}\frac{1}{\gamma'}$ \\
   {\footnotesize ADF$_{\text{Sh}}$}  & $1$ & $\frac{1}{1+\gamma'/r}$ & $\frac{r}{\gamma'}$ \\
	\hline
	\hline
\end{tabular}
\end{normalsize}
\end{table}

\section{Results}
\label{sec:resdis}

With the aid of simulations a good agreement between $\ensuremath{\text{AOC}}$ and $\ensuremath{\text{DQE}}$ is demonstrated.  Furthermore, reconstructions from a variety of simulated single-pixel set-ups and from an ADF-STEM experiment show close correspondence between MSE and $\ensuremath{\text{DQE}}$.  This justifies the use of the $\ensuremath{\text{DQE}}$ to derive optimal experimental settings and to determine when a CS set-up is preferable over a denoised Shannon scan.

\subsection{Agreement between DQE and $\ensuremath{\text{AOC}}$}
\label{sec:annuev}

The agreement between DQE and $\ensuremath{\text{AOC}}$ for single-pixel camera and ADF-STEM is evaluated under the assumption of three different noise models: Poisson noise only, Poisson noise and read-out noise and read-out noise only.

\subsubsection{Single-pixel}
\label{sec:crbdqesipi}

Two distinct single-pixel set-ups are investigated: PIX$_{\text{Di}}$ \ where the mirrors in the array take on discrete values of either $0$ or $1$, and PIX$_{\text{Fr}}$ \ where they take a fractional value between $0$ and $1$.

The test sample $x$ is the $100 \times 100$ Ramp-Discs phantom, displayed in Fig. \ref{fig:shepplogan}, yielding $N = 10000$. The intensities lie in the interval $[0.1, 1]$ to better mimic realistic experimental conditions; $\mu = 0.53$ and $\sigma = 0.18$. The sparse vector $s$ has approximately $N/10$ non-zero elements and $M$ is set to double that value, i.e. $2000$, to arrive at a reduction $r$ of $20$\%. The relative read-out noise $\gamma$ is set to $625$ and $I = 7.5 \times 10^5$, ensuring that $\ensuremath{p_{\text{opt}}}=0.10$ and that a CS-measurement with sensing matrix PIX$_{\text{Di}}$, $p = 0.01$ and combined Poisson and read-out noise has a $\ensuremath{\text{SNR}_{\text{out}}}^2$ of $10$ as calculated with (\ref{eq:snrout}).

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{phantoms.jpg}
  \caption{\label{fig:shepplogan} \emph{(a)}: The $100 \times 100$ Ramp-Discs phantom with gray values in the interval $[0.1, 1.0]$.  \emph{(b)}: The absolute values of the Laplacian.}
\end{figure}

The results for Poisson noise only are depicted in Fig. \ref{fig:sipipois}. Predictions by $\ensuremath{\text{DQE}}^{-1}$ agree well with the $\ensuremath{\text{AOC}}$, except for very low $p$ for sensing matrix PIX$_{\text{Fr}}$.

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{CRB-DQE_sM1-sM2_nM1.jpg}
  \caption{\label{fig:sipipois} $\ensuremath{\text{DQE}}^{-1}$ and $\ensuremath{\text{AOC}}$ vs. the fraction of on-pixels for the single-pixel set-up for Poisson noise only.}
\end{figure}

For these simulation settings the optimal value $\ensuremath{p_{\text{opt}}}$ for the case of simultaneous Poisson and read-out noise is $0.10$ for PIX$_{\text{Di}}$ \ and $0.16$ for PIX$_{\text{Fr}}$ \ as given by (\ref{eq:sipioptpoisrdt}) and (\ref{eq:sipioptpoisrdt2}) respectively. In Fig. \ref{fig:sipipoisrdt} it is shown how $\ensuremath{\text{AOC}}$ and $\ensuremath{\text{DQE}}^{-1}$ coincide for a wide range of $p$.

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{CRB-DQE_sM1-sM2_nM2.jpg}
  \caption{\label{fig:sipipoisrdt}  $\ensuremath{\text{DQE}}^{-1}$ and $\ensuremath{\text{AOC}}$ vs. the fraction of on-pixels for the single-pixel set-up for simultaneous Poisson and read-out noise. The values for $p$ are logarithmically spaced to better sample the region for low $p$.}
\end{figure}

The results for read-out noise only are depicted in Fig. \ref{fig:sipirdt}.  For both sensing matrices, PIX$_{\text{Di}}$ \ and PIX$_{\text{Fr}}$, $\ensuremath{\text{DQE}}^{-1}$ and $\ensuremath{\text{AOC}}$ agree well; yielding an optimum at $0.50$ and $0.67$, respectively.

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{CRB-DQE_sM1-sM2_nM3.jpg}
  \caption{\label{fig:sipirdt}  $\ensuremath{\text{DQE}}^{-1}$ and $\ensuremath{\text{AOC}}$ vs. the fraction of on-pixels for the single-pixel set-up for just read-out noise. }
\end{figure}

\subsubsection{ADF-STEM}
\label{sec:crbdqeadf}

The CS implementation of ADF-STEM, sensing matrix ADF$_{\text{CS}}$, is tested for all three noise models.

Simulations are carried out on the $100 \times 100$ Ramp-Discs phantom displayed in Fig. \ref{fig:shepplogan}. The simulation parameters are identical to those in Sec. \ref{sec:sipicare}, except that $\gamma'$ has been set to $0.5$ and $I = 2.5 \times 10^4$ so that the ADF$_{\text{CS}}$ -measurement with $p = 0.01$ and combined Poisson and read-out noise has a $\ensuremath{\text{SNR}_{\text{out}}}^2$ of $10$.

The values for $\ensuremath{\text{DQE}}^{-1}$ are compared to $\ensuremath{\text{AOC}}$ in Fig. \ref{fig:adfstemresults}.  A least absolute differences fit is used to scale both curves to each other, and an excellent agreement can be observed.

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{CRB-DQE_sM3_nM1-nM2-nM3.jpg}
  \caption{\label{fig:adfstemresults}  $\ensuremath{\text{DQE}}^{-1}$ and $\ensuremath{\text{AOC}}$ vs. the fraction of on-pixels for sensing matrix ADF$_{\text{CS}}$. All noise models: Pss stands for Poisson noise, rd-t for read-out noise.}
\end{figure}

\subsection{Agreement between DQE and MSE}
\label{sec:exre}

In this section Monte Carlo simulations and experiments are presented to illustrate that the settings predicted by the DQE as optimal do yield reconstructions with minimal mean squared error (MSE) when regularized with the $\ln L = \ensuremath{\text{E}}(\ln L)$ constraint in Sec. \ref{sec:comsen}.

\subsubsection{Monte Carlo simulations}
\label{sec:mocasi}

Single-pixel and ADF-STEM CS-measurements of the Ramp-Discs phantom were simulated with the same settings as in Sec. \ref{sec:crbdqesipi}.  Poisson noise and additive normal noise were added to the recordings as needed. For each value of $p$ ten measurements were simulated with different realizations of sensing matrix and noise.  As starting guess
\begin{eqnarray}
  \frac{ A^T y }{ I \langle A \rangle^2 N M } \label{eq:stague}
\end{eqnarray}
with a slight perturbation was used, where $\langle A \rangle$ denotes the average of all elements of $A$.

The MSEs were calculated with respect to the original phantoms and their averages plotted as a function of $p$ along with the sample standard deviation.  A first order least squares fit was used to match $\ensuremath{\text{DQE}}^{-1}$ to MSE.  That, contrary to Sec. \ref{sec:annuev}, a mere scaling does not suffice for a good agreement is an indication of the general biasedness of regularized estimators.

The results for the single-pixel camera with discrete mirror values (PIX$_{\text{Di}}$) in the presence of Poisson noise and read-out noise are presented in Fig. \ref{fig:sM1-nM2_sim}. The optimization ran for $50$ iterations, with $10$ subiterations for step 1; see App. \ref{sec:ElnL}. The MSEs show the same characteristic optimum for $p = 0.10$ as above. The $\ensuremath{\text{DQE}}^{-1}$ matches the MSE well and predicts the minimum.

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{MCRec_sM1_nM2.jpg}
  \caption{\label{fig:sM1-nM2_sim} $\ensuremath{\text{DQE}}^{-1}$ and $\ensuremath{\text{MSE}}$ vs. the fraction of on-pixels for the single-pixel camera with discrete on-values (PIX$_{\text{Di}}$) with Poisson noise and read-out noise. The values of $p$ are spaced logarithmically to sample the region around the optimum better. Compare to the results in Fig. \ref{fig:sipipoisrdt}.}
\end{figure}

The results for the single-pixel set-up with fractional mirror values (PIX$_{\text{Fr}}$) in the presence of just read-out noise are presented in Fig. \ref{fig:sM6-nM3_sim}. The optimization ran for $100$ iterations, with $10$ subiterations for step 1. The MSEs show the same characteristic optimum at about $0.67$ as above. The $\ensuremath{\text{DQE}}^{-1} $ matches the MSE well and can hence be used to predict the optimal experimental settings.

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{MCRec_sM2_nM3.jpg}
  \caption{\label{fig:sM6-nM3_sim} $\ensuremath{\text{DQE}}^{-1}$ and $\ensuremath{\text{MSE}}$ vs. the fraction of on-pixels for the single-pixel camera with fractional on-values (PIX$_{\text{Fr}}$) for read-out noise only. Compare to the results in Fig. \ref{fig:sipirdt}.}
\end{figure}

In Fig. \ref{fig:sipi_poiss_sim} results for the single-pixel camera with discrete on-values (PIX$_{\text{Di}}$) in the presence of just Poisson noise are presented.  The optimization ran for $50$ iterations, with $10$ subiterations for step 1. Despite systematic deviations, the $\ensuremath{\text{DQE}}^{-1}$ shows the same characteristic monotonic increase as the MSE and hence predicts the optimal settings well.

Ten values for $p$ were chosen, equidistantly spaced from $0.01$ to $0.90$.  To avoid purely numerical difficulties, the variable $\gamma$ was set to $0.05$ so that according to (\ref{eq:sipioptpoisrdt}) the optimal value for $p$ equals $0.001$, i.e. ten times smaller than the lowest value encountered.  This makes the ratio between the terms $c$ and $IAx$ in constraint (\ref{eq:clnL}) of the order of $10^{-4}$ for $p = 0.01$; for higher $p$ the ratio is even smaller.

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{MCrec_sM1_nM1.jpg}
  \caption{\label{fig:sipi_poiss_sim} $\ensuremath{\text{DQE}}^{-1}$ and $\ensuremath{\text{MSE}}$ vs. the fraction of on-pixels for the single-pixel set-up with discrete on-values (PIX$_{\text{Di}}$) for Poisson noise only. Compare to the results in Fig. \ref{fig:sipipois}.}
\end{figure}

\subsubsection{Experimental ADF-STEM}
\label{sec:expadfstem}

A gold nanorod was imaged in a FEI Titan$^3$ microscope operating in STEM mode at 300 kV.  An image $x_0$ with $256 \times 256$ pixels was raster scanned with an intensity $I_0 = 3.9\times 10^3$. After application of a $3 \times 3$ median filter, it served as ground truth to compute the MSE of the reconstructions; see Fig. \ref{fig:adfstem1}.a. Then, a $256 \times 256$ image $x_1$ was raster scanned with an intensity of $I _1 = 1.1 \times 10^2$; see Fig. \ref{fig:adfstem1}.b. At a standard deviation $\sqrt{c}$ of $0.32$~$\ensuremath{\text{e}^{-}}$ and $0.43$~$\ensuremath{\text{e}^{-}}$ for $x_0$ and $x_1$, respectively, the read-out noise was small, and this experiment exhibits almost pure Poisson noise.

Ten sensing matrices of type ADF$_{\text{CS}}$ \ were constructed with $p = 1/N$ and $M$ ranging from $N/10$ to $N$ in steps of $N/10$.  This corresponds to an inpainting set-up with a fraction $r$ of $M/N$ pixels available.  From $x_1$ and these ten matrices, ten measurements $y_1$ were synthesized.

The DQE for this set-up is calculated as laid out in App. \ref{sec:derdqe}.  However, since in this case the measurements are not taken at equal dose, (\ref{eq:snrinsp}) must be used for $\ensuremath{\text{SNR}_{\text{in}}}^2$ instead of (\ref{eq:snrinADF}); resulting in $\ensuremath{\text{DQE}} = M / N$.

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{ADF-STEM_CS.jpg}
  \caption{\label{fig:adfstem1} Experimental ADF-STEM data. \emph{(a)} Ground truth image $x_0$. \emph{(b)} Image $x_1$. \emph{(c)} Reconstruction from $M = N/10$ measurements, with $p = 1/N$. \emph{(d)} Reconstruction from $M = N$ measurements with $p = 1/N$, i.e. a denoising.}
\end{figure}

Again constraint (\ref{eq:clnL}) was used for the reconstructions.  The starting guesses were set according to (\ref{eq:stague}).  The reconstructions ran for $200$ iterations, with $10$ subiterations for step 1.  In Figs. \ref{fig:adfstem1}.c and \ref{fig:adfstem1}.d results are shown for $M = N/10$ and $M = N$.   Profiles over the central vertical line of the reconstructions are contrasted with the measurements in Fig. \ref{fig:adfstem2Profiles} to allow visual assessment of the reconstruction quality .

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{ProfilesADFSTEM.jpg}
  \caption{\label{fig:adfstem2Profiles}  Profiles and measurements for the central vertical line of the reconstructions in Fig. \ref{fig:adfstem1}, for $M/N = 0.1$ and $M/N = 1$. }
\end{figure}

For calculation of the MSEs, the reconstructions were registered to $x_0$ and the intensities were matched by a linear least squares fit to $x_0$.  The resulting MSEs are depicted in Fig. \ref{fig:adfstem2} where they are shown to match well with $\ensuremath{\text{DQE}}^{-1}$ after a linear transformation has been applied to the latter.

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{InPaintingADFSTEM.jpg}
  \caption{\label{fig:adfstem2}  After a linear transformation, the $\ensuremath{\text{DQE}}^{-1}$s match well to the MSEs of the reconstructions from the experimental ADF-STEM data. }
\end{figure}

\subsection{Main results: DQE analysis}
\label{sec:dqeres}

In this section optimal values $\ensuremath{p_{\text{opt}}}$ for $p$ are derived from the DQE; the results are summarized in Table \ref{tab:popt}. Furthermore, the $\ensuremath{\text{DQE}}$'s analytical tractability is deployed to investigate if the denoising of a Shannon scan is preferable over a full CS set-up, and under what circumstances this might be the case.

\begin{table}
\renewcommand{\arraystretch}{1.5}
\caption{Optimal Values for $p$ for Various Sensing Matrices and Noise Models.  See also (\ref{eq:sipioptpoisrdta}) and (\ref{eq:sipioptpoisrdta2}).}
\label{tab:popt}
\center
\begin{footnotesize}
\begin{tabular}{c | c c c }
  \hline
	\hline
	{\footnotesize Sensing} & \multicolumn{3}{c}{{\footnotesize Noise model}}\\
  {\footnotesize matrix}  & {\footnotesize Poisson} & {\footnotesize Poisson + read-out} & {\footnotesize read-out} \\
  \hline
   {\footnotesize PIX$_{\text{Di}}$}  & $1/N$ & $\sqrt{r\gamma/N}$ & $1/2$ \\
   {\footnotesize PIX$_{\text{Fr}}$}  & $1/N$ & $\frac{4}{\sqrt{6}}\sqrt{r\gamma/N}$ & $2/3$ \\
   {\footnotesize ADF$_{\text{CS}}$}  & $1/N$ & $1/N$ & $1/N$ \\
   {\footnotesize ADF$_{\text{Sh}}$}  & n.a. & n.a. & n.a. \\
	\hline
	\hline
\end{tabular}
\end{footnotesize}
\end{table}

\subsubsection{Single-pixel camera}
\label{sec:sipicare}

In the presence of just Poisson noise the DQE decreases monotonically with $p$, thus suggesting that the optimal value is the minimum $1/N$, which defines an inpainting set-up.  In the case of Poisson noise and read-out noise, the optimal value is obtained by equating the derivative of $\ensuremath{\text{DQE}}$ with respect to $p$ to zero, yielding
\begin{eqnarray}
  \ensuremath{p_{\text{opt}}} & = & \frac{r \gamma}{N} \( \sqrt{1 + \frac{N}{r\gamma}} - 1 \), \label{eq:sipioptpoisrdta} \\
        & \simeq & \sqrt{ \frac{r\gamma}{N} }, \quad \text{for} \ \sqrt{ \frac{r\gamma}{N} } \ll 1, \label{eq:sipioptpoisrdt}
\end{eqnarray}
for sensing matrix PIX$_{\text{Di}}$. For sensing matrix PIX$_{\text{Fr}}$ \ it holds that,
\begin{eqnarray}
  \ensuremath{p_{\text{opt}}} & = & 2\frac{r \gamma}{N} \( \sqrt{1 + \frac{2}{3} \frac{N}{r\gamma}} - 1 \), \label{eq:sipioptpoisrdta2} \\
        & \simeq & \frac{4}{\sqrt{6}}\sqrt{ \frac{r\gamma}{N} }, \quad \text{for} \ \sqrt{ \frac{r\gamma}{N} } \ll 1. \label{eq:sipioptpoisrdt2}
\end{eqnarray}
For just read-out noise an optimal value of $1/2$ is reached for PIX$_{\text{Di}}$, and $2/3$ for PIX$_{\text{Fr}}$. See Table \ref{tab:popt}

The DQE for the Shannon case is derived by setting $p = 1/N$ and $r = 1$ in the expression for PIX$_{\text{Di}}$ \ with simultaneous Poisson and read-out noise (Table \ref{tab:dqes}, first row, second column), yielding
\begin{eqnarray}
  \ensuremath{\text{DQE}}_{\text{Sh}} =  \frac{1}{N(1 + \gamma)}.
\end{eqnarray}

The CS set-up is treated for low read-out noise by evaluating the $\ensuremath{\text{DQE}}$ in the respective optimal values for $p$ (\ref{eq:sipioptpoisrdt}):
\begin{eqnarray}
  \ensuremath{\text{DQE}}_{\text{CS}} \simeq \frac{1}{N}, \quad \text{for} \ \sqrt{ \frac{r\gamma}{N} } \ll 1. \label{eq:dqecslowgam}
\end{eqnarray}
It is thus shown that in the absence of read-out noise ($\gamma = 0$), with only Poisson noise present, a CS recording contains the same amount of Fisher information as a Shannon scan.

In the limit of strong read-out noise (large $\gamma$) $\ensuremath{p_{\text{opt}}}$ in (\ref{eq:sipioptpoisrdta}) approaches $1/2$, and a lower bound is obtained by filling out $p = 1/2$ in the expression for the DQE:
\begin{eqnarray}
  \ensuremath{\text{DQE}}_{\text{CS}}^{\text{lb}} =  \frac{1}{2N + 4 r \gamma}.
\end{eqnarray}
From this it follows that if $\gamma$ exceeds $(1 - 4 r / N)^{-1} \simeq 1$, a CS reconstruction is preferred since then $\ensuremath{\text{DQE}}_{\text{CS}}^{\text{lb}} > \ensuremath{\text{DQE}}_{\text{Sh}}$.  In the limit of strong read-out noise the condition $\gamma > 1$ is met by construction.

Reconstructions from simulations following the settings in Sec. \ref{sec:crbdqesipi} were carried out to test the dependence of the MSE on the relative read-out noise $\gamma$ on CS recordings and Shannon scans.  The optimization ran for 50 iterations, with 10 subiterations for step 1.  For CS, $\gamma$ was varied from $10^{-1}$ to $10^{5}$, and following (\ref{eq:sipioptpoisrdta}) $p$ was set to $\ensuremath{p_{\text{opt}}}$ with values varying from $0.0014$ to $0.45$, respectively.  For the Shannon scans $\gamma$ was varied from $10^{-1}$ to $10^{1}$.

The results are depicted in Fig. \ref{fig:ShCSSipi}.  After a linear transformation has been applied to $\ensuremath{\text{DQE}}^{-1}$, it fits well to MSE.  For low noise both approaches yield comparable MSEs, but the much stronger rise for the Shannon scan shows CS is preferable in case of read-out noise.  Also, as predicted in (\ref{eq:dqecslowgam}), MSE for CS is approximately constant for the lower noise levels.

\begin{figure}
  \center
  \includegraphics[width = 0.99\linewidth]{ShVsCS_sipi.jpg}
  \caption{\label{fig:ShCSSipi}  MSE and $\ensuremath{\text{DQE}}^{-1}$ for reconstructions from Shannon (Sh) scans and from CS measurements for the single-pixel set-up.}
\end{figure}

\subsubsection{ADF-STEM}
\label{sec:adfstemre}

The expressions for the $\ensuremath{\text{DQE}}$s are given in Table \ref{tab:dqes} for ADF-STEM measurements. Contrary to the single-pixel set-up the optimal value for $p$ is independent of the noise model as for all models it holds that,
\begin{eqnarray}
  \frac{\partial}{\partial p} \ensuremath{\text{DQE}} \propto - \frac{1}{p^2},
\end{eqnarray}
indicating that $\ensuremath{\text{DQE}}$ is a monotonically decreasing function of $p$. This suggests the optimal value for $p$ is the minimum $1/N$ (see Table \ref{tab:popt}) and that an inpainting approach is preferred.

The quality of a CS reconstruction is compared to that of a denoised Shannon scan recorded with the same electron dose.  It can be shown that,
\begin{eqnarray}
  \text{if } p \geq \frac{1 + \gamma'/r}{ N } \text{, then } \ensuremath{\text{DQE}}_{\text{Sh}} \geq \ensuremath{\text{DQE}}_{\text{CS}}, \label{eq:dqe35}
\end{eqnarray}
where $\ensuremath{\text{DQE}}_{\text{CS}}$ and $\ensuremath{\text{DQE}}_{\text{Sh}}$ denote the $\ensuremath{\text{DQE}}$s for the CS and the Shannon case, defined respectively by sensing matrices ADF$_{\text{CS}}$ \ and ADF$_{\text{Sh}}$ \ for simultaneous Poisson and read-out noise (Table \ref{tab:dqes}, third and fourth row, second column).

In the absence of read-out noise, $\gamma'$ equals $0$ and condition (\ref{eq:dqe35}) is always met.  $\ensuremath{\text{DQE}}_{\text{Sh}} \geq \ensuremath{\text{DQE}}_{\text{CS}}$ then implies that a Shannon scan contains at least as much Fisher information as a CS measurement.  That the respective reconstructions yield approximately the same $\ensuremath{\text{MSE}}$ under equal dose conditions can be inferred from the results in Sec. \ref{sec:expadfstem} for experimental ADF-STEM where read-out noise was negligible.  Since these CS measurements were obtained by selecting $M$ pixels at random from a Shannon scan, the total dose for these CS measurements scales directly with $M$.  The results in Fig. \ref{fig:adfstem2} show that the $\ensuremath{\text{MSE}}$ is a linear function of $\ensuremath{\text{DQE}}^{-1} = N/M$ and hence of the inverse of the total dose.  This implies that for constant dose $\ensuremath{\text{MSE}}$ is constant as well, and hence equal to that of the denoised Shannon scan at $M/N = 1$.

\section{Discussion}
\label{sec:dis}

Rigorous as the $\ensuremath{\text{AOC}}$ is, it lacks some generality as it yields results for just the test object and the particular realization of the sensing matrix $A$, and requires knowledge of the support in the sparse basis. In contrast, the DQE, although more heuristic in nature, is an analytical function of the experimental conditions and alleviates some of the $\ensuremath{\text{AOC}}$'s drawbacks: the test object enters through just its mean value, only the variance of the sensing matrix entries is needed and knowledge of the support is not necessary.

A caveat is that for too few on-pixels the Fisher information matrix becomes singular, which means no unbiased estimators are possible \cite{li2012} and the $\ensuremath{\text{AOC}}$ cannot be computed.  This is information that the $\ensuremath{\text{DQE}}$ cannot deliver, and its predictions therefore only hold on the condition of the Fisher information matrix being non-singular.

That regularized estimators are in general biased is reflected in the fact that a linear fit is needed to match $\ensuremath{\text{DQE}}^{-1}$ to the MSE of the reconstructions, instead of the mere scaling that sufficed for matching to the $\ensuremath{\text{AOC}}$.  Nevertheless, the $\ensuremath{\text{DQE}}$ still predicted the optimal experimental settings accurately, thus suggesting that also biased estimators perform best with measurements with maximum Fisher information.

\section{Conclusions}
\label{sec:con}

In this paper the performance of various CS set-ups was assessed under the constraint of constant total illumination and compared to that of a denoised Shannon scan with the same dose.  The A-optimality information criterion $\ensuremath{\text{AOC}}$ was chosen as a measure of the amount of Fisher information in the measurements.  With the aid of simulations, the heuristic quantity detective quantum efficiency $\ensuremath{\text{DQE}}$ was shown to track the $\ensuremath{\text{AOC}}$ accurately.  Also the mean squared error (MSE) of CS reconstructions from experimental and simulated recordings was well tracked by the $\ensuremath{\text{DQE}}$.

The $\ensuremath{\text{DQE}}$'s analytical tractability was then used to show that for the investigated sensing matrices and in the absence of read-out noise, i.e. with only Poisson noise present, compressed sensing does not raise the amount of Fisher information in the recordings above that of a Shannon sampled signal.  As a consequence, reconstruction results yield a comparable MSE when both data sets are treated with the same algorithm. This result holds for both investigated systems, but is particularly surprising for the single-pixel camera, as the Shannon scan makes use of only $1/N$ of the total dose.   This is considered of fundamental importance here as read-out noise can be viewed as a mere engineering problem for particles with sufficiently high energies. This might temper the high expectations for beam damage reduction that were laid out in the TEM community.

The $\ensuremath{\text{DQE}}$ was also used to optimize the experimental designs, i.e. the fraction $p$ of on-pixels for best reconstruction quality as a function of particle dose, read-out noise and other experimental parameters.  In the presence of Poisson noise these results, summarized in Table \ref{tab:popt}, differ markedly from the optimal $p = 1/2$ often tacitly assumed in literature.  When there is only Poisson noise an inpainting set-up ($p = 1/N$) is optimal in all investigated systems.  No matter the noise model, $p = 1/N$ is optimal for ADF-STEM.  When there is only read-out noise $p = 1/2$ and $p = 2/3$ are optimal if the on-values in the single-pixel camera are discrete or fractional, respectively.  A combination of Poisson noise and read-out noise yields an optimum between these extremes.

redpajama_set_name: RedPajamaArXiv


text:
Chicago Teachers Strike For Smaller Classes and More School Resources
By Ana Connery October 18, 2019
Jesse Sharkey, President of the Chicago Teachers Union, at the Chicago Teachers Union Rally on 10-14-19. Charles Edward Miller from Chicago, United States [CC BY-SA 2.0]
As Windy City teachers began day two of their first strike since 2012, 300,000 public school students remained out of school Friday.
The list of concerns among the 25,000 educators on strike will probably sound familiar, as they tend to be some of the biggest pain points in public schools: smaller class sizes, more school counselors and support staff, and equity for disadvantaged students.
A Chicago Sun-Times poll taken just before the strike showed parents are largely sympathetic to teachers' concerns, even as families have had to adjust.
While schools remain open, buses aren't running, and children aren't technically required to attend school. "We understand that's hard for parents," said Jesse Sharkey, president of the Chicago Teachers Union, to a group of reporters at the start of day two of the strike. "But it's a short-term disruption for what we hope is a long-term commitment to educational justice in this city." For every child whose school is affected but still made it to school, administrators are left scrambling to fill students' days with lessons so they don't fall behind.
Day one ended with no resolutions after 10 hours of negotiating. In a press conference, Chicago Mayor Lori Lightfoot pointed to a lengthy counter-offer the city had previously released. "It provides a 16 percent pay raise for all employees,"' Mayor Lightfoot said. "It would lift up lowest-paid workers immediately. On average, support staff will see a 38 percent pay raise over the life of the (five-year) contract under the current offer." More money would be set aside for counselors and nurses and $1 million would go towards reducing class sizes among all grade levels.
Several similar strikes have taken place around the country this year, and some have lasted up to two weeks. To help support parents as negotiations continue in the coming days, dozens of community centers, aquariums, churches, YMCAs, and Boys and Girls Clubs of Chicago have opened to students.
schoolagersschoolsteacher payteachers
Ana Connery
The former Content Director at Parenting, parenting.com and several other brands, Ana Connery is a writer and content strategist whose work appears in USA Today, Reader's Digest, Real Simple, Cafe Mom/The Stir, Momtastic, and others.
Photo: NASA
First All-Female Space Walk Just Happened—Here's What It Means For Our Daughters
October 18, 2019 3 Mins Read
Creatas / Photo Images Canva Pro
Researchers Say Would-Be Moms (and Dads) Should Stop Drinking Alcohol 6 Months Or More Before Conception
Stacey Rupolo / Chalkbeat
Joe Mabel, CC BY-SA 4.0 via Wikimedia Commons [cropped]
Photo by Allison Shelley/The Verbatim Agency for EDUimages

redpajama_set_name: RedPajamaCommonCrawl


text:
Search Provider Directory
AuroraMed Cares Blog
Get Covered America™
EMS Provider Resources
Donate Life Colorado
Hospital Campuses
Philosophy of Patient Care
Tobacco-Free Environment
Volunteer Application Process
The Medical Center of Aurora Get Directions
Centennial Medical Plaza
Saddle Rock ER
Medical Center of Aurora /
Sub Menu About Awards & Honors Charity Care Contact Us Media Center Donate Life Colorado Executive Team Hospital Campuses Legal Mission, Vision & Values Patient Stories Philosophy of Patient Care Phone Directory Tobacco-Free Environment Annual Reports Volunteer Application Process Locations
At The Medical Center of Aurora, patients are our first priority. We take extreme measures to ensure high quality, safe care in the most comfortable setting possible.
Highlights About The Medical Center of Aurora
Metro Denver's first community hospital to earn two-time Magnet Recognition for nursing excellence
Primary Stroke Certification (The Medical Center of Aurora South Campus)
Two accredited Chest Pain Centers (South Campus and Centennial Medical Plaza)
Named Colorado's ONLY 2016 Leapfrog Top General Hospital
Recognized as the #4 hospital in the Denver metro area and the #4 hospital in Colorado by U.S. News & World Report's Best Hospitals Report (2014-2015, 2017-2018)
Received 'A' grades from The Leapfrog Group (Fall 2015, Fall 2016, Spring 2017)
Level II Trauma Center at our South Campus
Level III NICU at our South Campus
Received the Emergency Nurses Association Lantern Award Recipient for 2013-2016, one of only nine hospitals in the country
Saddle Rock ER received Press Ganey's 2016 Guardian of Excellence Award for Outstanding Performance in Patient Experience
State-of-the-art Heart Care Tower on South Campus
Community Hospital Cancer Program accreditation from American College of Surgeons' Commission on Cancer
NAPBC-accredited Breast Cancer Care Center
Rocky Mountain Hospital for Children affiliation
Affiliate of HealthONE, Denver's largest healthcare system
Read More About our Awards & Honors
About The Medical Center of Aurora
The Medical Center of Aurora, the first community hospital in the Denver Metro area to receive two-time Magnet designation for nursing excellence by the American Nurses Credentialing Center (ANCC), is a 346-bed acute care hospital located in Aurora, Colorado. The Medical Center of Aurora is comprised of six campuses in Aurora and Centennial, Colo., including the Main Campus, located at Interstate 225 and Mississippi, the North Campus Behavioral Health and Wellness Center, Centennial Medical Plaza, Saddle Rock ER, Spalding Rehabilitation Hospital, Spalding Rehabilitation at P/SL, and a medical office building at Green Valley Ranch. The Main Campus facility is a Level II Trauma Center with Primary Stroke Certification and Chest Pain Center accreditation, serving the eastern metro area and I-70 corridor. The Medical Center of Aurora received 'A' grades from The Leapfrog Group (Fall 2015, Fall 2016, Spring 2017), was named Colorado's only 2016 Leapfrog Top General Hospital, was recognized as the #4 hospital in the Denver metro area and the #4 hospital in Colorado by U.S. News & World Report (2014-2015, 2017-2018), and was one of only nine hospitals in the country to receive the Lantern Award for Excellence in Emergency Room Care by the Emergency Nurses Association (2013).
Need a Physician? Call (303) 575-0055.
1501 S Potomac Street
About TMCA
Patient & Visitor Resources
Volunteering at TMCA
Follow us on Facebook Follow us on LinkedIn Follow us on YouTube Read Our Blog
Quick Links About Us--Contact Us--Maps & Directions--Careers--Physician Careers--About TMCA--MediaResources--Billing--Online Pre-Registration--Find a Doctor--MyHealthOne Patient Portal--Patient & Visitor Resources--Volunteering at TMCA--Charity Care


text:
The Founding
On 24 January 1791, the Rev. Jeremy Belknap invited nine like-minded Bostonians to join him in creating what they would call simply, "The Historical Society," now the Massachusetts Historical Society, the oldest organization in the United States devoted to collecting materials for the study of American history.
As he envisioned it, the society would become a repository and a publisher collecting, preserving,and disseminating resources for the study of American history. Through their pledges of family papers, books, and artifacts from their personal collections, the founding members made the Society the nation's first historical repository by the end of their initial meeting. With the appearance of their first title at the start of 1792, they also made the MHS the nation's first institution of any description to publish in its field.
In the absence of any other American historical repositories in the 1790s, the MHS took on a broadly national role, one still apparent in both its collections and its publications. As other historical institutions were founded elsewhere, including the New-York Historical Society in 1804 and the American Antiquarian Society in 1812, the Society started to direct special attention to Boston, Massachusetts, and New England. The continuing legacy of its early years as the nation's only repository of American history, however, is a program of collections and activities of national and international importance.
The Society Today
The MHS is an invaluable resource for the study of American history, life, and culture. Its collections tell the story of America through over twelve million documents, artifacts, and national treasures, including the personal papers of three presidents—John Adams, John Quincy Adams, and Thomas Jefferson. Since 1791, the Society has nurtured and spread knowledge and the appreciation of American history by preserving and enriching its collections, providing tools and services to support research, and cultivating scholarship. The MHS is committed to the principle that knowledge of our nation's past is fundamental to its future. We desire to reach a broad audience and to illustrate for them the importance of history in understanding change and continuity in our world.
Over the past decade, the MHS has made great strides in making its resources available to a wider public. This has been greatly enhanced by the use of technology, especially through an improved website. ABIGAIL, the Society's online catalog, and collection guides open the collections to all, and digitization efforts have made increasing amounts of material available to researchers. Library visitation is growing because of the on-line presence of the MHS and an increase in the number of research fellowships offered. A new endowed acquisitions fund has made it possible to add to collections at a time when purchasing items has become more competitive.
Public programs and exhibitions play a central role in reaching the public and dispensing knowledge. The MHS offers a full roster of engaging programs including talks by established and emerging historians, history makers, and public leaders on topics that range from current events to the lives of individuals who shaped our country. Exhibitions highlight the Society's collections or important themes and events, attracting a growing audience.
The Society's education initiatives, designed to enhance the teaching of history to school-age audiences, have grown substantially. Annually, the MHS provides workshops to over five hundred teachers from across the country focused on the use of primary documents to enrich the classroom experience. Teacher fellows use the MHS collections to develop new lesson plans that are added to our increasing catalog of online educational resources available to educators everywhere. The MHS is now the state sponsor of Massachusetts History Day, which engages over a thousand students statewide each year. These efforts are augmented by a number of on-site student programs.
Through its activities, the MHS has built a national and international network of scholars who work in the fields in which we focus. The MHS has added fellowships and seminars and presented much-praised conferences. Publications are attractive and include exhibition catalogs to further knowledge of MHS collections. The Adams Papers documentary edition has increased its output in addition to producing several popular works and providing increased digital access to unpublished materials and online tools.
By expanding the range of MHS activities to embrace public programs and exhibitions, the organization has been building a community of Members who share an interest in history, enjoy the social as well as the intellectual attraction of events at the MHS, spread the word through friends and family, and build public support for history and for the MHS.
The MHS collections and the community of scholars, researchers, teachers, and writers we serve provide the foundation for the Society's educational and public history programs. By building interest in and support for American history, these programs directly serve the MHS mission in themselves, but they also strengthen the Society as an organization dedicated to continuing to preserve and expand its collections and other research activities. After a decade of transformation and growth the Society finds itself poised to become an even greater influence in shaping the future of our nation.
MHS Timeline
Board of Trustees & Council of Overseers
Historical Perspectives on Today's World: Our Nation's Founders and Today's Political Challenges
30Jan 6:00PM 2020
This program will be held at the Edward M. ...
Our Founding Fathers were progressive for their time in establishing a new nation. Many of them grappled with the same issues that we face today, including political ...
MHS Tour
The History and Collections of the MHS
1Feb 10:00AM 2020
The History and Collections of the Massachusetts Historical Society Tour is a 90-minute docent-led walk through our public rooms. The tour is free, open to the public, ...
Peter J. Gomes Memorial Book Prize Ceremony
3Feb 6:00PM 2020
There is a pre-talk reception at 5:30.
Please join us for a special evening in which historian Christine DeLucia will receive the 2019 Gomes Prize for Memory Lands: King Philip's War and the Place of ...
See our calendar for all events
Join us for a program this week! Here is a look at what is going on: - Tuesday, 29 January, 5:15 PM: Better Teaching through Technology, 1945-1969, with Victoria Cain, Northeastern ...
Founder to Founder
Like so many good stories here at the Historical Society, it began with a reference question. Jeremy Belknap, hunting through his sources, asked Vice President John Adams for some help. Belknap, the ...
The New-England Courant


"Aw, you're good for nothing," taunted Yaeko as she again bested her 8-year-old kid brother, Sadao, in their playful tussle, his precociousness not quite enough to help him overcome the tomboy in her, much less the fact that she was older by two years. And although these tender and warm-hearted sisterly joshings would stay in Sadao's consciousness through the years, they would come to find their greater consequence in Yaeko herself.
Sadao Munemori's father, Kametaro, had migrated from Hiroshima to California after the turn of the century. His wife, Nawa, followed shortly with their baby, Yuriko. Then came the rest of the family: Isao (Bob), Yaeko, Sadao and Kikuyo (Keech), all born in Los Angeles.
Kametaro died in 1938, so he was spared the agony and the humiliation of the forced relocation of the Japanese people from their West Coast homes to inland centers as a result of Japan's December 7, 1941, attack upon Pearl Harbor. Along with over a hundred thousand Japanese, citizens and non-citizens alike, the Munemori family was swept out of its home the following March. Then consisting of the mother, son Bob, and two daughters (Yuriko was in Japan), the family was displaced to the Manzanar relocation center. Sadao, who had volunteered for the Army a month before Pearl Harbor, had been inducted just the month before and was in an Army training center.
His first two years of military training were spent in such scattered locations as Arkansas, Illinois and Minnesota. In January 1944, he was sent south to Camp Shelby in Mississippi and there was subsequently assigned to Company A, 442d Regimental Combat Team, then in training for overseas combat duty.
In one of his first letters from Shelby to the family in Manzanar, he recalled that he was only 19 when he had volunteered for the Army and that it "was a big decision I had gone over and over again at nights when you all were sleeping. I think I did right by enlisting because my home is here in the U.S. and it helped a lot to bind the family together more than ever."
He had other things to say. From having observed young recruits "actually cry for not having taken advice from their parents," he had come to the conclusion that "Your mother is NEVER wrong." And, comparing himself to those "kids" as he called those 19-through-21 year olds, he had a confession to make, of sorts: "I haven't cried because you know what kind of guy I am. I'm just a good-for-nothing like Yaeko used to say."
Yaeko, now Mrs. Albert Yokoyama and a resident of Honolulu since 1946, recalls that particular time when the young Sadao was at the point of losing yet another fight with her and began to pout: "You just wait. When I grow up, they're going to name a ship after me. And I'm not going to let you ride on it." Like the reverberations of a temple bell that keep ringing in the ears long after the last striking. Sadao's words keep coming back to Yaeko whenever her thoughts dwell on him, which is often, inasmuch as he is the first nisei recipient of the congressional Medal of Honor. And the pulsations out of the past come to her all the more vividly because of her flippant rejoinder: "I don't care. I wouldn't ride on your ship anyway."
Sadao was in one of the first group of replacements for the 100th Infantry Battalion then fighting at Anzio. He left the 442nd in Shelby in April and arrived at the Anzio beachhead a month later and was assigned to Company A.
By then the 100th had been in combat in Italy for nine months, having entered the Italian theater in September 1943 at Salerno Bay, south of Naples. By January, it was engaged in the tremendous battle for Cassino, the town with the towering Benedictine monastery standing guard over the southern gateway to Rome. The beachhead at Anzio was designed as an "end-around" maneuver to break the enemy's grip upon Cassino and that highway to Rome, but the undertaking was going askew in the face of stiff enemy opposition. The 100th suffered horrendous combat losses.
But, on June 5, Rome ultimately did fall into Allied hands. It was after that battle that the 442d arrived in Italy, at which point the 100th became the 1st Battalion of the larger nisei unit. Three months later the 100/442 was withdrawn from the Italian theater and shifted over to France where they played a heroic role in the rescue of the "Lost Battalion" in the forests above Bruyeres, a little town up near the northeast corner by the Franco German border. After the battle, Sadao wrote to Yaeko that "the scenery is very beautiful here, but all the beautiful forests remind me of now is terror, destruction and the painful cries of my buddies in agony. We all hate the Nazis over here, but every front line man respects the German soldier because he really is an artist in that line."
Following several months of light patrol duty in southern France in the Maritime Alps, the 100/442 was pulled out and secretly returned to Italy. General Mark Clark, 5th Army Commander, greeted the return of the 100th to his fold with these words: "You, of all battalions, I pledge, will share in the great victory ahead." But ahead of that victory lay the enemy's nigh-impregnable Gothic Line, a defensive barrier built into the northern Apennines mountain range blocking the entrance into the Po Valley. It had repulsed repeated 5th Army assaults for nearly half a year, much as Cassino a year earlier had withstood similar attempts for five months.
But then, in one of the war's most magnificent assaults upon an enemy stronghold, the 100/442 scaled the mountain heights of the Gothic Line in the early morning hours of April 5, 1945, and reached the top undetected by the enemy. At 0500 hours (5 a.m.) they were in position. Following a massive artillery barrage, they attacked-the 100th's objective, Hill "Georgia" while other units of the 442d attacked "Florida." With Company A in the lead, the initial push advanced several hundred yards, then faltered as the enemy, recovering from the artillery barrage and the surprise appearance of the Americans, fought back with, machine guns and pistols, rifles and grenades. Although the early morning darkness made the enemy fire inaccurate, their fire nevertheless took its toll. But as one soldier dropped, another took his place and so the attack continued until the hills had been secured. The time was 0532. In the wash of the concentrated attack lay the mangled body of Pfc. Sadao Munemori in a shell crater.
His squad leader injured, Pfc. Munemori had taken charge of the leading squad. With him were Pfc. Akira Shishido of Paia, Maui, and Pvt. Jimi Oda, Ogden, Utah. The following is Pfc. Shishido's eyewitness account of the ongoing fight: "We advanced nearer the objective until another machine gun opened up right there. Pvt. Oda and I scrambled into a shell crater and Pfc. Munemori crawled back and joined us. The Germans began hurling grenades again. Ten or 12 landed near our crater but we were unhurt by the explosions."
Sadao Munemori was posthumously awarded the Congressional Medal of Honor for "conspicuous gallantry and intrepidity involving risk of life above and beyond the call of duty in action against the enemy."
The undertaking upon the mountain bastions of Hills Georgia and Florida in which Sadao gave his life brings to mind the stroke of boldness that characterized Ichi-no-tani in 1184, one of the great battles in Japanese history. The Minamoto and Taira forces were locked in combat for supremacy of the country. Taira no Munemori had built a military stronghold around Fukuhara, or Ichi-no-tani, on the shores of Settsu province on the Inland Sea, across from modern-day Osaka. With control of the sea in their hands and the high mountains behind forming a natural barrier against land attacks, the Taira felt secure in their base spread along the narrow shoreline. But on that early morning in 1184, Minamoto no Yoshitsune led a group of horsemen around and up the mountain. There, confronted by the steep sides at whose base lay the enemy's camp, Yoshitsune then let his horses slip and slide their way down, the warriors clinging to the mounts while whispering bits of encouragement into their ears. In that manner did Yoshitsune achieve complete surprise. Disorganized by the unexpected appearance of the foe behind them, the retaliation of the Taira was ineffectual. Crushed, they took to flight.
Eight centuries later, the all-night climb of the 100/442 up the steep sides of the Apennines to surprise the enemy and rout him out of his long held redoubt can be viewed as a feat of boldness and daring in the manner of Yoshitsune at Ichi-no-tani.
That heroic dimension of the human spirit was enjoined by the Army in a ceremony without precedence in the history of the United States when in 1948 at the Brooklyn Army Base in New York, the speedy 10,000-ton troopship "Wilson Victory" the very ship that had brought back the men and colors of the 100/442 to New York on their triumphant homecoming from Italy after the war-was redesignated the "Pvt. Sadao S. Munemori."
When the ship made its first call to Honolulu shortly after the redesignation action, Yaeko was invited to be the first to board it. Memories crowded upon her as she awaited the eventful day. . .
She was an R. N. and had left Manzanar in March 1943 under sponsorship to work in The Madison General Hospital in Wisconsin. It was there, on April 20, 1945, that a telegraph operator called her to read a telegram from her brother, Bob, in Manzanar: KEEP STIFF UPPER LIP RECEIVED MILITARY WIRE SADAO KILLED IN ACTION 5 APRIL ITALY.
Just three days earlier, she had written Sadao telling him that "I was certainly glad to hear from you again and was really surprised to hear you are back in Italy. Then, I take it, you are with the 5th Army in the northern section of Italy, fighting hard. Do be careful."
"We had sunrise service this morning," he had written in a letter dated April 1, "and I saw some boys get baptized. Gee but it was nice not to be fighting and able to have a service like we did today with a band." It was to be his last letter home.
Young Sadao had excitedly dashed off to go swimming at the community pool with his friend, a Norwegian lad. But when he returned he went straight to his room without a word to anyone. They all wondered why and, after a while. Yaeko went to check and found him on his bed, face down, but not asleep. She felt his trunks-dry! Why, he hadn't even gone swimming! Reluctantly, the boy explained that there was a big sign at the entrance to the pool: NO JAPS ALLOWED. But there were no tears in him. Yaeko wondered why.
Her parents loved Japanese music so they had stacks of records. The children smashed them all. They also smashed the cameras shredded their Japanese textbooks and notebooks. The evacuation instructions read "no pets" so they tied their dog to a post. And on that Sunday, as they rode off in the Army truck headed for the evacuation center, the dog began yelping and straining at his leash. Long after house and dog were out of sight, she could still hear him crying. . . .
Now, as she prepared to board the ship, her feet could barely carry her up the gangplank-her body tensed from the anticipation and the intoxicating heart-pounding drama of the moment as Sadao's pouting cry of exasperation and resignation came echoing over the space and time of thousands of miles and many a year: "And-l'm-not-going-to-let-you-ride-on-it."
Nawa Munemori died in 1966 and the safekeeping of Sadao's medal fell to the remaining members of the family. But since they too, in time, would pass away, they decided that the best and most appropriate place for the permanent safekeeping of the medal would be in the U.S. Army Museum at Ft. DeRussy. Sadao's medal and picture now stand alongside the memorabilia of the many other heroes of Hawaii.
from Shelby - "These Hawaiian buddies of mine sure treat me nice."
from New York port of embarkation - "One thing about these guys I'm with is that they are always happy and cheerful. I'm just gonna have to visit my buddies in Hawaii after the war."
from Anzio - "The 100th Inf. boys are really a swell bunch of guys and they give us good advice which soaks in our brains faster than anything in the world."
from France - "All of us boys are already thinking of the future and the fellows want me to come to Hawaii and visit them for sure. That's one thing that I'll have to do when I return. You know how I couldn't get along too good with Japanese boys back home. Well I can get along pretty good with these guys because they don't try to hold back anything. Yes, Keech! I'm gonna have to visit them after the war."
And, from a hospital bed in France in January '45 where he was recovering from a case of yellow jaundice, he wrote Yaeko that he'd be out in a few days and back with boys, "if there are still some guys I know left. The 100th isn't the same outfit it used to be when I joined it at Anzio because it's made up mostly of replacements - but it's still a very powerful unit."
One of those replacements was Stanley Izumigawa from Maui who recently wrote The Hawaii Herald that: "Spud, as he asked we call him, joined us only a few months after we ourselves had joined the outfit as replacements. We were then near the bombed out town of Cisterna, in the Alban foothills on the way to Rome. We quickly found that he did not fit our image of the typical 'kotonk.' He was very friendly, outgoing, accepting, and it didn't take him long to pick up pidgin and become one of us."
An evidence of the mutual affection is in the nickname itself. Yaeko recalls that although Sadao back home used to love potatoes, it was only after he had joined the 100th that moniker began to appear in his letters.
Spud is buried in the veterans section of the Evergreen Cemetery in Los Angeles but a part of him, represented by the Medal of Honor, has come to rest in Hawaii . . . the place he longed to visit, the home of many of his buddies, the place where they, like him, also lie consecrated in hallowed hometown final resting places.
Ben Tamashiro's article was reprinted courtesy of the Estate of Ben Tamashiro and The Hawaii Herald. Copyright retained by the Estate of Ben Tamashiro and The Hawaii Herald.


text:
Gråkindad bambusångare (Phylloscopus poliogenys) är en asiatisk fågel i familjen lövsångare inom ordningen tättingar.

Utseende och läten
Gråkindad bambusångare är en 10-11 cm lång fågel. Den har vit ögonring, grått huvud och ett svagt markerat ögonbrynsstreck. Ovansidan är olivgrön, undersidan gul. Jämfört med liknande glasögonbambusångaren är den grå på örontäckare och tygel, medan hakan är vit. Glasögonbambusångaren har istället gröna örontäckare samt gul tygel och haka. Sången består av korta strofer med varierade visslande toner.

Utbredning och systematik
Arten förekommer i bergsskogar från norra Indien till sydvästra Kina, Myanmar och Indokina. Den behandlas som monotypisk, det vill säga att den inte delas in i några underarter. Fågeln är nära släkt med glasögonbambusångaren (P. intermedius). Studie av mitokondrie-DNA visar att populationen i Himalaya kan utgöra en annan art än den i Yunnan i Kina respektive södra Vietnam, de senare två också väl differentierade genetiskt.

Släktestillhörighet
Bambusångarna placeras traditionellt i släktet Seicercus. DNA-studier visar dock att arterna i Seicercus inte är varandras närmaste släktingar, där vissa arter istället står närmare arter i Phylloscopus. Olika auktoriteter hanterar detta på olika vis. De flesta expanderar numera Phylloscopus till att omfatta hela familjen lövsångare, vilket är den hållning som följs här. Andra flyttar ett antal Phylloscopus-arter till ett expanderat Seicercus.

Familjetillhörighet
Lövsångarna behandlades tidigare som en del av den stora familjen sångare (Sylviidae). Genetiska studier har dock visat att sångarna inte är varandras närmaste släktingar. Istället är de en del av en klad som även omfattar timalior, lärkor, bulbyler, stjärtmesar och svalor. Idag delas därför Sylviidae upp i ett antal familjer, däribland Phylloscopidae. Lövsångarnas närmaste släktingar är familjerna cettisångare (Cettiidae), stjärtmesar (Aegithalidae) samt den nyligen urskilda afrikanska familjen hylior (Hyliidae).

Levnadssätt
Gråkindad bambusångare häckar i frodig undervegetation i övre delen av den varma tempererade lövskogszonen. Den födosöker nära marken efter insekter. Fågeln häckar mellan april och juni i Himalaya och åtminstone i april och maj i Vietnam. Arten är stannfågel, men flyttar till lägre regioner vintertid.

Status och hot
Arten har ett stort utbredningsområde och en stor population med stabil utveckling och tros inte vara utsatt för något substantiellt hot. Utifrån dessa kriterier kategoriserar internationella naturvårdsunionen IUCN arten som livskraftig (LC). Världspopulationen har inte uppskattats men den beskrivs som lokalt vanlig.

Noter

Externa länkar

 Läten på xeno-canto.org

Lövsångare
Fåglar i orientaliska regionen

redpajama_set_name: RedPajamaWikipedia


We already wrote about Gboard 6.1 Beta, which adds a few notable features including Google Translate integration and an improved theme picker. Since that post, we've received tips about more changes in the update, so let's take a look at a few of them.
Before this update, tapping on the microphone button in Gboard would cause the keyboard itself to collapse and show a voice typing interface in its place. This animation is rather slow if you have a lower-end phone, and if you want to go back to the keyboard, you have to close the voice typing popup and wait for the keyboard to re-appear.
In Gboard 6.1, tapping the microphone button keeps the full keyboard open, only showing an indicator for voice typing on the top right. Not only does this work better than the old solution, but you can simply tap anywhere on the keyboard to stop voice input.
Next up is GIF suggestions. When Google Keyboard was updated to Gboard last year, one of the new major features was the ability to insert GIFs (only with compatible apps). Gboard 6.1 takes that to another level by adding GIF results to the suggestions bar. I don't think I would use this much, but I'm sure at least some of you are psyched about it.
Gboard 6.1 is still in beta, which means you have to either join the beta program on the Play Store or download the APK from APKMirror to try it out. You can also wait for the update to leave beta, which I'm sure isn't too far off.


The Menoire relatively early maturing, bends muscat grape flavors. Kind of nature unmistakably recognizable of wine. Due to the rapid development primeur wines suitable for yielding.
Its color medium purple, red.
Aromas of pure fruit flavors, particularly cherries and blackberries and a sense of spiciness: eucalyptus and red pepper are also displayed.
Palate: Dry. With a light body & vibrant acidity this wine shows a fine tannic structure with elegance & balance.
The perfect wine for BBQ & easy drinking, so just perfect answer to the younger generation.


Hen pecked hubby's are so hard to spot..
Just how catty are you, little lady?
Building his own community with murderous love.
What to look for when someone isnt 'quite right'...even in their innocence.
A humble life is greatness on its own.
One man proves you dont need a piece of corporate america and grand things to be perfectly content in life.
Back to my horror, if just this little bit. Blood, pain, fear. Ah, so seductive.
What used to be safe is now something deadly. Every generation it moves and changes its dark beast.
Love spent years can bring desolation when one lover moves on. Given time, a whole new world is waiting, if you just open the door.
Take a breath, plan your moves, and even the darkest of times can move along easy.
Yes, why cant a bloodsucking vampire enjoy a nice evening on her porch in the swamps and enjoy from lemonade?
You cant force love, no matter how strongly you feel it, you cant make the object of your affections feel the same.
Dont expect to be treated like a queen when really you're just a dirty little secret.
Finally, a little bit of light in a cold dark world for one man.
Grandmas are usually the best..
Memories of lost times with Grandma are usually treasures to be preserved and cherished.
Beauty can be found everywhere, even in lost memories and death. Saying good bye does not end things.
I was young and stupid. I admit it.
When you have it all, why do you long for more? Or for whats forbidden?
Even the bright and dazzling have rough edges. When not kept in check, chips and cracks appear.
You give and get in life. Which, in some cases, can be deadly.
What comes around goes around, even if malicious intent is not involved.
Fire lives and breathes...and she wants you.
Would you be brave enough?
This is based on a true life event.
A woman finds a key tag. Curiosity runs rampant, but common decency leaves her questions unanswered.
Life gives and takes, brutally.
What happens when good people have terrible things happen to them?
Going to the lake usually ensures a good time and happy memories, right?
A man ponders just what to do with his wife, their finances and daily living. Deep thoughts indeed.
This is a somber story, of a coroner who takes what comes through her doors and creates stories for them, to give them a life that many never will know.
Genesis and Addison plot their escape, sharing their aversion to one another along the way.
Stranger things come in to light, adding questions on top of questions.
What happens when you fall into a pit of zombies?
Genesis and Addison scramble to safety, only to find that they were never all that safe to begin with. Is everything working against them tonight?
The two crewmates assess their current predicament, none too happy with their situation.
Addison and Genesis struggle to get to higher ground and out of the reach of the amassing zombies wanting their nights meal.
Addison takes her first strides into The Great War...World War One. There, she has an idea that will change her way of thinking and her future actions forever.
Our little vampiress makes new discoveries, and meets a new mysterious stranger.
Addison loses everyone, left to fend for herself.
Addison tries to reclaim her social standing with a failed attempt.
Our little vampiress prepares for her future and the sanctity of her beloved property.
Our little newly made vampire finds her way back home, only to be met with horrible and devastating results.
A little glimpse of our lead character, Addison, and her life before and after becoming ensnared and captured by a malevolent being. From this, she is set on her 'Road'.


text:
Disclaimer: Many projects on here are open source, and many don't show any ads. However, for all legal purposes (and to avoid any legal problems), this privacy policy applies to everything on this subdomain (ryan778.github.io).
If you require any more information or have any questions about our privacy policy, please feel free to contact me by email at ryanzh778 [at] gmail.com.
At ryan778.github.io, the privacy of our visitors is of extreme importance. This privacy policy document outlines the types of personally identifiable information (PII) is received and collected by ryan778.github.io and how it is used.
Although ryan778.github.io does not directly make use of log files, Google Analytics is used on this site and does log some information on users. The information inside the log files includes internet protocol (IP) addresses, type of browser, Internet Service Provider (ISP), date/time stamp, referring/exit pages, and number of clicks to analyze trends, administer the site, track user's movement around the site, and gather demographic information. IP addresses, and other such information are not linked to any information that is personally identifiable. More information can be found under the "Other Cookies" section of this privacy policy.
Ryan778.github.io occasionally uses cookies to store information about visitors preferences, record user-specific information on which pages the user access or visit, customize web page content based on visitors browser type or other information that the visitor sends via their browser.
Google, as a third party vendor, uses cookies to serve ads on ryan778.github.io.
Google's use of the DART cookie enables it to serve ads to users based on their visit to ryan778.github.io and other sites on the Internet.
Google Adsense, our advertising partner, may use cookies and web beacons on some parts of this site. They use this technology on the advertisements and links that appear on ryan778.github.io sent directly to your browsers. They automatically receive your IP address when this occurs. Other technologies (such as cookies, JavaScript, or Web Beacons) may also be used by the third-party ad networks to measure the effectiveness of their advertisements and / or to personalize the advertising content that you see. Ryan778.github.io has no access to or control over these cookies that are used by third-party advertisers.
You should consult the Google Adsense privacy policy for more detailed information on their practices as well as for instructions about how to opt-out of certain practices. Ryan778.github.io's privacy policy does not apply to, and we cannot control the activities of, such other advertisers or web sites. The Google Adsense privacy policy is available at https://www.google.com/privacy_ads.html.
This site uses Google Analytics which is one of the most widespread and trusted analytics solution on the web to help understand how you use the site and ways to improve your experience. These cookies may track things such as how long you spend on the site and the pages that you visit so we can continue to produce engaging content.
You can opt-out of having made your activity on the Service available to Google Analytics by installing the Google Analytics opt-out browser add-on. The add-on prevents the Google Analytics JavaScript (ga.js, analytics.js, and dc.js) from sharing information with Google Analytics about visits activity. For more information on Google Analytics cookies, see the official Google Analytics page.
If you wish to disable cookies, you may do so through your individual browser options. More detailed information about cookie management with specific web browsers can be found at the browsers' respective websites.
© 2020 Ryan Zhang. All Rights Reserved.


Employee Stock Ownership Plan (ESOP) Definition | Human Resources (HR) Dictionary | MBA Skool-Study.Learn.Share.
ESOPs are the plans which offer company's stocks to their employees at rate, which is below the market rate.
Hence, this concludes the definition of Employee Stock Ownership Plan (ESOP) along with its overview.
Browse the definition and meaning of more terms similar to Employee Stock Ownership Plan (ESOP). The Management Dictionary covers over 7000 business concepts from 6 categories.
Prev: Employee Rights.. Next: Employee Survey..


If you doesn't configure any Groovy installation and select (Default) option, plugin will fallback into calling just groovy command, assuming you have groovy binary on the default path on given machine.
The system groovy script, OTOH, runs inside the Jenkins master's JVM. Thus it will have access to all the internal objects of Jenkins, so you can use this to alter the state of Jenkins. It is similar to the Jenkins Script Console functionality.
System groovy jobs has access to whole Jenkins, therefore only users with admin rights can add system groovy build step and configure the system groovy script. Permissions are not checked when the build is triggered (i.e. also uses without admin rights can also run the script). The idea is to allow users run some well defined (defined by admin) system tasks when they need it (e.g. put slave offline/online, when user wants to start some debugging on slave). To have Jenkins instance secure, the support for Token macro plugin has to be switched off, see section bellow.


In 1974 some farmers were digging a water well near Xi'an, China. They accidentally made one of the greatest archeological discoveries of the twentieth century, the terracotta army of China's first emperor, Qin Shi Huang (秦始皇). Construction of the necropolis began shortly after Qin Shi Huang rose to power at age 13 in 246 BC. By the time of his death in 210 BC, the three pits containing the Terracotta Army contained 8000 soldiers, 130 chariots with 510 horses and 150 cavalry horses. This army was built to accompany the emperor in the afterlife.
I spent most of a day visiting the Terracotta Army. For me, the site lived up to the hype. The most impressive part was the minute level of detail. Every soldier had a unique face. Each strand of hair was individually carved. There was even tread on the bottoms of their shoes. Besides the opportunity to look at the soldiers themselves, there was a lot of information about the history of the army and its discovery. In fact, the Terracotta Army was one of my favorite sites in all of China.


text:
Марчиуэ () — посёлок в Чили. Административный центр одноимённой коммуны. Население — 2 208 человек (2002).   Посёлок и коммуна входит в состав провинции Карденаль-Каро и области Либертадор-Хенераль-Бернардо-О'Хиггинс.

Территория — 660 км². Численность населения — 7 308 жителя (2017). Плотность населения — 11,1 чел./км².

Расположение
Посёлок расположен в 86 км на запад от административного центра области города Ранкагуа и в 37 км на восток от административного центра провинции  города Пичилему.

Коммуна граничит:
 на севере — c коммунами Литуэче ,  Ла-Эстрелья
 на востоке — с коммуной Пичидегуа
 на юго-востоке — c коммуной Пералильо
 на юге — c коммуной Пуманке
 на западе — c коммуной Пичилему

Демография
Согласно сведениям, собранным в ходе переписи 2017 г  Национальным институтом статистики (INE),  население коммуны составляет:

Важнейшие населенные пункты

Ссылки
 Официальный сайт коммуны
Коммуна Марчиуэ (citypopulation.de)

Примечания

Коммуны Чили
Города Чили