  The Anscombe transform offers an approximate conversion of a Poisson random
variable into a Gaussian one. This transform is important and appealing, as it
is easy to compute, and becomes handy in various inverse problems with Poisson
noise contamination. Solution to such problems can be done by first applying
the Anscombe transform, then applying a Gaussian-noise-oriented restoration
algorithm of choice, and finally applying an inverse Anscombe transform. The
appeal in this approach is due to the abundance of high-performance restoration
algorithms designed for white additive Gaussian noise (we will refer to these
hereafter as "Gaussian-solvers"). This process is known to work well for high
SNR images, where the Anscombe transform provides a rather accurate
approximation. When the noise level is high, the above path loses much of its
effectiveness, and the common practice is to replace it with a direct treatment
of the Poisson distribution. Naturally, with this we lose the ability to
leverage on vastly available Gaussian-solvers.
  In this work we suggest a novel method for coupling Gaussian denoising
algorithms to Poisson noisy inverse problems, which is based on a general
approach termed "Plug-and-Play". Deploying the Plug-and-Play approach to such
problems leads to an iterative scheme that repeats several key steps: 1) A
convex programming task of simple form that can be easily treated; 2) A
powerful Gaussian denoising algorithm of choice; and 3) A simple update step.
  Such a modular method, just like the Anscombe transform, enables other
developers to plug their own Gaussian denoising algorithms to our scheme in an
easy way. While the proposed method bares some similarity to the Anscombe
operation, it is in fact based on a different mathematical basis, which holds
true for all SNR ranges.

Computer Vision and Pattern Recognition;Optimization and Control