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Plug-and-Play (PnP) methods are efficient iterative algorithms for solvingill-posed image inverse problems. PnP methods are obtained by using deepGaussian denoisers instead of the proximal operator or the gradient-descentstep within proximal algorithms. Current PnP schemes rely on data-fidelityterms that have either Lipschitz gradients or closed-form proximal operators,which is not applicable to Poisson inverse problems. Based on the observationthat the Gaussian noise is not the adequate noise model in this setting, wepropose to generalize PnP using theBregman Proximal Gradient (BPG) method. BPGreplaces the Euclidean distance with a Bregman divergence that can bettercapture the smoothness properties of the problem. We introduce the BregmanScore Denoiser specifically parametrized and trained for the new Bregmangeometry and prove that it corresponds to the proximal operator of a nonconvexpotential. We propose two PnP algorithms based on the Bregman Score Denoiserfor solving Poisson inverse problems. Extending the convergence results of BPGin the nonconvex settings, we show that the proposed methods converge,targeting stationary points of an explicit global functional. Experimentalevaluations conducted on various Poisson inverse problems validate theconvergence results and showcase effective restoration performance.

Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problems