用于泊松逆问题的收敛 Bregman 即插即用图像复原
Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problems
AI总结：
针对泊松逆问题，本文基于 BPG 提出收敛的 Bregman PnP 框架，设计 Bregman Score Denoiser 并证明两种算法收敛到显式全局泛函驻点。
摘要：
即插即用（PnP）方法是求解病态图像逆问题的高效迭代算法。PnP 方法通过在近端算法中使用深度高斯去噪器替代近端算子或梯度下降步骤得到。当前 PnP 方案依赖于具有 Lipschitz 梯度或闭式近端算子的数据保真项，这不适用于泊松逆问题。基于高斯噪声并非该设置下适当噪声模型的观察，我们提出使用 Bregman Proximal Gradient（BPG）方法推广 PnP。BPG 用 Bregman 散度替代欧氏距离，能够更好地捕捉问题的平滑性质。我们引入了 Bregman Score Denoiser，它针对新的 Bregman 几何进行专门参数化和训练，并证明其对应于一个非凸势函数的近端算子。我们提出两种基于 Bregman Score Denoiser 的 PnP 算法，用于求解泊松逆问题。通过将 BPG 的收敛结果扩展到非凸设置，我们表明所提方法收敛，目标是显式全局泛函的驻点。在多种泊松逆问题上进行的实验评估验证了收敛结果，并展示了有效的复原性能。
英文摘要：
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.
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