隨插即用方式的影像復原演算法

Abstract

隨著圖像復原演算法的發展，許多人都同意先驗（prior）在提高復原性能方面扮演了很重要的角色。最近發展出的基於隨插即用 (Plug-and-Play) 的方法，將基於模型的圖像復原方法和基於學習的方法的優點相結合，因其高效能和易於實現而受到廣泛關注。 本論文探討基於隨插即用的圖像復原演算法，這是一種對於解決圖像復原問題來說很有效的方法。第一章介紹了本文的主題。第二章探討了將隨插即用先驗應用於成像問題中，包括建立圖像復原模型、圖像復原的最佳化問題、隨插即用架構以及相關工作。第三章涵蓋了基於可變分割演算法的隨插即用圖像復原，包括交替方向乘子法（ADMM）、半二次分割演算法（HQS）和加速迭代收縮/閾值演算法（FISTA），以及它們的收斂性分析和實驗結果。在第四章中，我們研究了與隨插即用相關的演算法，像是去噪正則化 (RED) 和多重代理共識平衡 (MACE)，以及它們的收斂性分析和實驗結果。最後，第五章是本文的結論。總體而言，這篇論文全面介紹了基於隨插即用的圖像復原演算法和其相關的演算法以及它們在各種圖像復原任務中的應用。

With the development of the image restoration algorithms, one can admit that priors play in a important role in improving restoration performance. The recently developed plug-and-play prior method, which incorporates the advantages of model-based image restoration method and the learning-based method, owes its popularity to its efficiency and the ease of implementation. This paper focuses on Plug-and-Play based Image Restoration Algorithms, which are a promising and effective approach to address image restoration problems. Chapter 1 provides an introduction to the topic. In Chapter 2, the Plug-and-Play prior in imaging problem is discussed, including the modeling for Image Restoration, Optimization problem in Image Restoration, Plug-and-play framework, and related work. Chapter 3 covers Variable splitting algorithms for plug-and-play image restoration, including Alternating Direction Method of Multipliers (ADMM), Half Quadratic Splitting algorithm (HQS) and Fast Iterative Shrinkage/Thresholding Algorithm (FISTA), as well as their convergence analysis and experiment results. In Chapter 4, we also investigate PnP-related algorithms such as Regularization by Denoising (RED) and Multi-Agent Consensus Equilibrium (MACE), along with their convergence analysis and experiment results. Finally, Chapter 5 concludes the paper. Overall, this paper provides a comprehensive overview of plug-and-play based image restoration algorithms and Plug-and-Play related algorithms, as well as their applications in various image restoration tasks.