It's well-known that inverse problems are ill-posed and to solve them meaningfully one has to employ regularization methods. Traditionally, the most popular regularization approaches are Variational-type approaches, i.e., penalized/constrained functional minimization. In recent years, the classical regularization approaches have been replaced by the so-called plug-and-play (PnP) algorithms, which copies the proximal gradient minimization processes, such as ADMM or FISTA, but with any general denoiser. However, unlike the traditional proximal gradient methods, the theoretical analysis and convergence results have been insufficient for these PnP-algorithms. Hence, the results from these algorithms, though empirically outstanding, are not well-defined, in the sense of, being a minimizer of a Variational problem. In this paper, we address this question of ``well-definedness", but from a different angle. We explain these algorithms from the viewpoint of a semi-iterative regularization method. In addition, we expand the family of regularized solutions, corresponding to the classical semi-iterative methods, to further generalize the explainability of these algorithms, as well as, enhance the recovery process. We conclude with several numerical results which validate the developed theories and reflect the improvements over the traditional PnP-algorithms, such as ADMM-PnP and FISTA-PnP.

中文翻译：

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从不同角度解读即插即用（PnP）算法

众所周知，逆问题是不适定的，为了有意义地解决它们，必须采用正则化方法。传统上，最流行的正则化方法是变分型方法，即惩罚/约束函数最小化。近年来，经典的正则化方法已被所谓的即插即用 (PnP) 算法所取代，该算法复制了近端梯度最小化过程，例如 ADMM 或 FISTA，但具有任何通用降噪器。然而，与传统的近端梯度方法不同，这些 PnP 算法的理论分析和收敛结果不足。因此，这些算法的结果虽然在经验上很出色，但在作为变分问题的最小化器的意义上并没有明确定义。在本文中，进一步概括这些算法的可解释性，并增强恢复过程。我们以几个数值结果作为结论，这些结果验证了所开发的理论并反映了对传统 PnP 算法（例如 ADMM-PnP 和 FISTA-PnP）的改进。进一步概括这些算法的可解释性，并增强恢复过程。我们以几个数值结果作为结论，这些结果验证了所开发的理论并反映了对传统 PnP 算法（例如 ADMM-PnP 和 FISTA-PnP）的改进。