用深度去噪器解决成像逆问题,提升重建质量。
Solving Imaging Inverse Problems Using Plug-and-Play Denoisers: Regularization and Optimization Perspectives
- 将学习到的去噪器作为隐式先验嵌入迭代算法
- 证明了在特定条件下算法仍能收敛
- 适合从事图像重建与深度学习结合的研究者
成像逆问题在医学成像、遥感和显微镜等领域至关重要。近年来,数据驱动的正则化方法逐渐成为主流,显著提升了重建质量。其中,利用学习到的图像去噪器作为隐式先验,嵌入迭代重建算法,形成所谓的插件式(Plug-and-Play, PnP)方法。本文系统综述了这类方法的发展,从图像去噪和传统正则化出发,讨论如何将近端分裂算法(如ADMM、PGD)中的近端算子替换为学习型去噪器,并分析其收敛条件。文中还探讨了Tweedie公式在最优高斯去噪与梯度估计之间的联系,为正则化-去噪(RED)及基于扩散模型的后验采样方法奠定基础。重点强调了保证收敛所需的去噪器结构假设,如非扩张性、Lipschitz连续性和局部齐次性。同时讨论了实际设计中的去噪器架构选择与加速策略。
原文摘要 · Abstract (English)
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 chapter 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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。