Plug-and-Play (PnP) methods are efficient iterative algorithms for solving
ill-posed image inverse problems. PnP methods are obtained by using deep
Gaussian denoisers instead of the proximal operator or the gradient-descent
step within proximal algorithms. Current PnP schemes rely on data-fidelity
terms that have either Lipschitz gradients or closed-form proximal operators,
which is not applicable to Poisson inverse problems. Based on the observation
that the Gaussian noise is not the adequate noise model in this setting, we
propose to generalize PnP using theBregman Proximal Gradient (BPG) method. BPG
replaces the Euclidean distance with a Bregman divergence that can better
capture the smoothness properties of the problem. We introduce the Bregman
Score Denoiser specifically parametrized and trained for the new Bregman
geometry and prove that it corresponds to the proximal operator of a nonconvex
potential. We propose two PnP algorithms based on the Bregman Score Denoiser
for solving Poisson inverse problems. Extending the convergence results of BPG
in the nonconvex settings, we show that the proposed methods converge,
targeting stationary points of an explicit global functional. Experimental
evaluations conducted on various Poisson inverse problems validate the
convergence results and showcase effective restoration performance.

本论文提出了两种基于 Bregman 得分去噪器的 PnP 算法，用于解决 Poisson 反问题，并证明了该方法收敛于明确全局功能的稳定点。

Poisson 反问题中的收敛 Bregman 插值播放图像修复

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

Plug-and-Play methods constitute a class of iterative algorithms for imaging
problems where regularization is performed by an off-the-shelf denoiser.
Although Plug-and-Play methods can lead to tremendous visual performance for
various image problems, the few existing convergence guarantees are based on
unrealistic (or suboptimal) hypotheses on the denoiser, or limited to strongly
convex data terms. In this work, we propose a new type of Plug-and-Play
methods, based on half-quadratic splitting, for which the denoiser is realized
as a gradient descent step on a functional parameterized by a deep neural
network. Exploiting convergence results for proximal gradient descent
algorithms in the non-convex setting, we show that the proposed Plug-and-Play
algorithm is a convergent iterative scheme that targets stationary points of an
explicit global functional. Besides, experiments show that it is possible to
learn such a deep denoiser while not compromising the performance in comparison
to other state-of-the-art deep denoisers used in Plug-and-Play schemes. We
apply our proximal gradient algorithm to various ill-posed inverse problems,
e.g. deblurring, super-resolution and inpainting. For all these applications,
numerical results empirically confirm the convergence results. Experiments also
show that this new algorithm reaches state-of-the-art performance, both
quantitatively and qualitatively.

本文提出了一种新型的 Plug-and-Play 方法，使用半二次分裂作为正则器，将梯度下降步骤实现为由深度神经网络参数化的功能。作者证明了该算法是一个收敛的迭代方案，可应用于各种形式的逆问题，比如去模糊、超分辨率和修复等，达到与最先进的方法相当的性能。