Inverse problems lie at the heart of modern imaging science, with broad applications in areas such as medical imaging, remote sensing, and microscopy. Recent years have witnessed a paradigm shift in solving imaging inverse problems, where data-driven regularizers are used increasingly, leading to remarkably high-fidelity reconstruction. A particularly notable approach for data-driven regularization is to use learned image denoisers as implicit priors in iterative image reconstruction algorithms. This survey presents a comprehensive overview of this powerful and emerging class of algorithms, commonly referred to as plug-and-play (PnP) methods. We begin by providing a brief background on image denoising and inverse problems, followed by a short review of traditional regularization strategies. We then explore how proximal splitting algorithms, such as the alternating direction method of multipliers (ADMM) and proximal gradient descent (PGD), can naturally accommodate learned denoisers in place of proximal operators, and under what conditions such replacements preserve convergence. The role of Tweedie's formula in connecting optimal Gaussian denoisers and score estimation is discussed, which lays the foundation for regularization-by-denoising (RED) and more recent diffusion-based posterior sampling methods. We discuss theoretical advances regarding the convergence of PnP algorithms, both within the RED and proximal settings, emphasizing the structural assumptions that the denoiser must satisfy for convergence, such as non-expansiveness, Lipschitz continuity, and local homogeneity. We also address practical considerations in algorithm design, including choices of denoiser architecture and acceleration strategies.

翻译：逆问题处于现代成像科学的核心，在医学成像、遥感和显微成像等领域具有广泛应用。近年来，成像逆问题的求解范式发生了转变，数据驱动的正则化方法日益普及，实现了显著的高保真重建。数据驱动正则化中一个特别值得关注的方法，是将学习型图像去噪器作为隐式先验嵌入迭代图像重建算法中。本综述全面概述了这类强大且新兴的算法——通常被称为即插即用方法。我们首先简要介绍图像去噪与逆问题的背景知识，随后回顾传统正则化策略。接着探讨邻近分裂算法（如交替方向乘子法和邻近梯度下降法）如何自然地接纳学习型去噪器以替代邻近算子，并分析此类替换保持收敛性的条件。文中讨论了Tweedie公式在连接最优高斯去噪器与分数估计中的作用，这为去噪正则化及近期基于扩散的后验采样方法奠定了理论基础。我们阐述了即插即用算法在去噪正则化框架和邻近算子框架下的收敛性理论进展，重点分析了去噪器为满足收敛所需的结构性假设（如非扩张性、Lipschitz连续性和局部齐次性）。同时探讨了算法设计中的实际考量，包括去噪器架构的选择与加速策略。