Fast Active Set Methods for Online Spike Inference from Calcium Imaging
Fluorescent calcium indicators are a popular means for observing the spiking activity of large neuronal populations. Unfortunately, extracting the spike train of each neuron from raw fluorescence calcium imaging data is a nontrivial problem. We present a fast online active set method to solve this sparse nonnegative deconvolution problem. Importantly, the algorithm progresses through each time series sequentially from beginning to end, thus enabling real-time online spike inference during the imaging session. Our algorithm is a generalization of the pool adjacent violators algorithm (PAVA) for isotonic regression and inherits its linear-time computational complexity. We gain remarkable increases in processing speed: more than one order of magnitude compared to currently employed state of the art convex solvers relying on interior point methods. Our method can exploit warm starts; therefore optimizing model hyperparameters only requires a handful of passes through the data. The algorithm enables real-time simultaneous deconvolution of O(10 5 ) traces of whole-brain zebrafish imaging data on a laptop.
This paper introduces a new algorithm for inferring the spiking pattern from a univariate calcium-imaging time-series. Calcium imaging is a popular technique for recording activity from thousands of individual neurons simultaneously.  An neuronal spike causes a sharp increase but a slow decrease in the observed calcium image signal.  Most neuroscience applications require deconvolving the observed signal to recover the underlying spikes.  This paper follows quite closely the exponential-decay and noise model [5], introducing an active set algorithm that solves this model much faster than previous methods (they report a 20x difference from previous competitor). They show the speed gain (with apparent successful deconvolution) on both simulated and real data, though it is hard to tell if the quality of spike inference has been improved or degraded.   
 I enjoyed reading this paper, as it provides a clear and well argued algorithmic alternative for the spike inference problem.  The authors take a different approach than previous work solving the model for this problem, by modifying the isotonic regression into a locally constrained estimation problem. The authors make a strong case that algorithmic acceleration could potentially broaden the experimental scenarios in which large-scale calcium imaging can be used.    Main Comments: 1. The paper really only focuses on fitting the non-negative LASSO problem described in Eq (3)  [l 105] or on providing the best reconstruction of the path [see how accuracy is measured in Figure 3].  The reconstruction is never directly measured in terms  of the spikes location or strength. It is telling that the "goal of calcium deconvolution" is defined in terms of this  penalised optimisation, rather than in terms of the underlying spikes.   These are related goals, but are not exactly the same. Note that reconstruction equivalency to other algorithms is taken for granted.   In particular, its unclear that the hard noise constraint in Part 4 induces better recovery of the spikes  compared to other values. A different metric than signal correlation should be used to estimate this.   2. How sensitive is the hard-constraint of part-4 to the exactness of the model. The mean shape in the model (an exponential decay) is quite restrictive; what happens if the model mildly deviates from it? Is the noise still well estimated?    Minor comment:  The model in Eq 2, if based on previous literature should be referenced [is it from Ref 5?].