Poisson inverse problems by the Plug-and-Play scheme

Arie Rond*, Raja Giryes, Michael Elad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)96-108
Number of pages13
JournalJournal of Visual Communication and Image Representation
Volume41
DOIs
StatePublished - 1 Nov 2016
Externally publishedYes

Funding

FundersFunder number
Google
Seventh Framework Programme
European Research Council320649
Israel Science Foundation1770/14
Intel Collaboration Research Institute for Computational Intelligence

    Keywords

    • Image processing
    • Poisson deblurring
    • Poisson denoising

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