Poisson inverse problems by the Plug-and-Play scheme

The easy-to-compute Anscombe transform offers a conversion of a Poisson random variable into a variance stabilized Gaussian one, thus becoming handy in various Poisson-noisy inverse problems. Solution to such problems can be done by applying this transform, then invoking a high-performance Gaussian-noise-oriented restoration algorithm, and finally using an inverse transform. This process works well for high-SNR images, but when the noise level is high, it loses much of its effectiveness. This work suggests a novel method for coupling Gaussian denoising algorithms to Poisson noisy inverse problems. This approach is based on a general approach termed “Plug-and-Play-Prior”. Deploying this to Poisson inverse-problems leads to an iterative scheme that repeats an easy treatable convex programming task, followed by a powerful Gaussian denoising This method, like the Anscombe transform, enables to plug Gaussian denoising algorithms for the Poisson-oriented problem, and yet, it is effective for all SNR ranges.