Plug and Play Splitting Techniques for Poisson Image Restoration

TL;DR

This paper introduces PnPSplit+, a novel plug-and-play method for Poisson image restoration that provides closed-form solutions for deblurring, ensuring convergence and high performance in noisy and blurred conditions.

Contribution

It extends the PIDSplit+ algorithm to Poisson data, enabling closed-form solutions and convergence guarantees in PnP schemes for Poisson image restoration.

Findings

Achieves high-quality restoration under severe noise and blur

Provides closed-form deblurring solutions without iterative solvers

Ensures convergence with a firmly non-expansive denoiser

Abstract

Plug and Play (PnP) methods achieve remarkable results in the framework of image restoration problems for Gaussian data. Nonetheless, the theory available for the Gaussian case cannot be extended to the Poisson case, due to the non-Lipschitz gradient of the fidelity function, the Kullback-Leibler functional, or the absence of closed-form solution for the proximal operator of such term, leading to employ iterative solvers for the inner subproblem. In this work we extend the idea of PIDSplit+ algorithm, exploiting the Alternating Direction Method of Multipliers, to PnP scheme: this allows to provide a closed form solution for the deblurring step, with no need for iterative solvers. The convergence of the method is assured by employing a firmly non expansive denoiser. The proposed method, namely PnPSplit+, is tested on different Poisson image restoration problems, showing remarkable performance even in presence of high noise level and severe blurring conditions.