发表机构
Indian Institute of Technology Roorkee（印度理工学院鲁尔基分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出加速即插即用Davis-Yin分裂法，统一分析非凸图像重建问题，结合FISTA加速、线搜索与PnP去噪，实验验证其收敛性和重建质量。
AI 中文摘要
本文研究了一类在成像应用中出现的结构化非凸非光滑优化问题，其目标函数为三个函数之和。我们考虑了Davis-Yin分裂方法、一种FISTA型加速变体、拟牛顿线搜索方法以及即插即用（PnP）扩展来求解该问题。我们在温和假设下，基于Davis-Yin包络发展了一个统一的收敛性分析，包括Kurdyka-Łojasiewicz性质。在此框架内，我们建立了迭代序列子序列和全局收敛到稳定点的结论，以及残差收敛速率。我们展示了所提方法在图像恢复和低秩矩阵补全问题上的性能。对于低秩矩阵补全，我们在合成数据和公开数据集上进行了实验，以评估恢复精度和效率。在成像任务（包括图像去模糊）中，我们使用峰值信噪比（PSNR）比较了几种算法变体的收敛行为和重建质量。结果表明，FISTA加速和线搜索方法改善了收敛性，而PnP去噪器提升了图像质量，且所提方法在矩阵补全任务上保持竞争力。
英文摘要
In this work, we study a class of structured non-convex and non-smooth optimization problems arising in imaging applications, where the objective is the sum of three functions. We consider the Davis-Yin splitting method, a FISTA-type accelerated variant, along with a quasi-Newton line-search method and a plug-and-play (PnP) extension to solve the problem. We develop a unified convergence analysis based on the Davis-Yin envelope under mild assumptions, including the Kurdyka-Łojasiewicz property. Within this framework, we establish subsequential and global convergence of the iterates to stationary points, together with residual convergence rates. We demonstrate the performance of the proposed methods on image restoration and low-rank matrix completion problems. For low-rank matrix completion, we perform experiments on both synthetic data and public datasets to evaluate recovery accuracy and efficiency. In imaging tasks, including image deblurring, we compare the convergence behaviour and reconstruction quality of several algorithmic variants using peak signal-to-noise ratio (PSNR). The results show that FISTA-acceleration and line-search methods improve convergence, while PnP denoisers enhance image quality, and the proposed methods remain competitive on matrix completion tasks.
