Inverse problems in image processing are typically cast as optimization tasks, consisting of data fidelity and stabilizing regularization terms. A recent regularization strategy of great interest utilizes the power of denoising engines. Two such methods are the Plug-and-Play Prior (PnP) and Regularization by Denoising (RED). While both have shown state-of-the-art results in various recovery tasks, their theoretical justification is incomplete. In this paper, we aim to enrich the understanding of RED and its connection to PnP. Towards that end, we reformulate RED as a convex optimization problem utilizing a projection (RED- PRO) onto the fixed-point set of demicontractive denoisers. We offer a simple iterative solution to this problem, and establish a novel unification of RED-PRO and PnP, while providing guarantees for their convergence to the globally optimal solution. We also present several relaxations of RED-PRO that allow for handling denoisers with limited fixed-point sets. Finally, we demonstrate RED-PRO for the tasks of image deblurring and super-resolution, showing improved results with respect to the original RED framework.

该研究论文介绍了一种用于求解图像逆问题的新方法，根据投影最小化噪声引入一个基于稳定化策略的新的前景偏好正则化算法，受限的极小极大问题以及RED-PRO算法进行研究并给出了数学公式模型，然后给出了数值模拟实验结果。

通过固定点投影去噪正则化（RED-PRO）