PnP-IPA：一种用于非凸成像问题的可证明收敛的即插即用不精确近端算法
PnP-IPA: A Provably Convergent Plug-and-Play Inexact Proximal Algorithm for Nonconvex Imaging Problems
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中文总结 AI 辅助
研究针对非凸成像问题，介绍PnP-IPA算法，提出新分裂策略和替代优值函数，克服现有方法局限，基于Kurdyka-Lojasiewicz性质建立全局收敛，实验证明其在图像去模糊中有实际优势，能实现最优参数调整和鲁棒收敛。
中文摘要 AI 辅助
即插即用（PnP）方法已成为解决成像逆问题的高效范例，用深度去噪器取代正则化项的传统邻近算子。尽管经验上成功，但为PnP算法建立严格收敛保证仍是重大挑战。基于梯度步（GS）去噪器的现有可证明方法存在理论和实践限制。本文介绍PnP-IPA，一种克服这些瓶颈的新型优化方案。提出新的分裂策略不精确评估缩放隐式正则化器的近端算子，设计新型替代优值函数驱动类似Armijo的回溯线搜索。基于Kurdyka-Lojasiewicz性质，在不对正则化参数做假设的情况下建立到非凸目标驻点的全局收敛。高斯和柯西噪声下图像去模糊的大量数值实验证明了PnP-IPA的实际优势。
英文摘要
Plug-and-Play (PnP) methods have emerged as a highly effective paradigm for solving imaging inverse problems by replacing traditional proximity operators of regularization terms with highly expressive deep denoisers. While empirically successful, establishing rigorous convergence guarantees for PnP algorithms remains a major challenge. Existing provable approaches based on the Gradient-Step (GS) denoiser suffer from theoretical and practical limitations, such as restrictive bounds on the regularization parameter, rigid step-size rules, and the inability to handle nonconvex data-fidelity terms. In this paper, we introduce PnP-IPA (Plug-and-Play Inexact Proximal Algorithm), a novel optimization scheme that overcomes these bottlenecks. We propose a new splitting strategy that evaluates the proximal operator of the scaled implicit regularizer inexactly. To enable adaptive step-size selection without exact objective evaluations, we design a novel surrogate merit function that successfully drives an Armijo-like backtracking line-search. Relying on the Kurdyka-Lojasiewicz property, we establish global convergence to a stationary point of the nonconvex objective without imposing any assumption on the regularization parameter. Extensive numerical experiments on image deblurring under both Gaussian and Cauchy noise demonstrate the practical advantages of PnP-IPA. By effectively lifting previous theoretical constraints, our method allows for optimal parameter tuning, yielding state-of-the-art restoration quality and robust convergence even in nonconvex regimes.
