Tingting Liu, Le Xing and Zhonggui Sun
　

Liaocheng University  
　

Abstract

Plug-and-play (PnP) is a powerful framework that applies off-the-shelf denoisers to regularize imaging inverse problems in an iterative style. Remarkably, in several restoration applications, this kind of regularization exhibits promising behaviors. Among the algorithms derived from the framework, the ISTA-based (PnP-ISTA) has attracted much attentions due to the effectiveness and simple update rule in iterations. And its convergence analysis has become a fundamental topic. Most recently, the theoretical convergence of PnP-ISTA with kernel denoisers has been established, where the kernel is generic (relaxing the reliance on special properties) and thus beneficial for wider applications. In there, the convergence proof focuses on fixed kernels. Note that, the denoisers with adaptive kernels usually achieve more powerful performance than those with fixed ones. Inspired by the preliminary observation, we extend the fixed kernelsto adaptive onesfor the denoisers in PnP-ISTA. Under a mild assumption, we prove the convergence theoretically. Meanwhile, for inpainting, an important scenario, we broaden the interval of the step size from (0,1) to (0, 2) , which still guarantees the convergence. Experimental results agree with our theoretical conclusions.

　

Paper

T. Liu, L. Xing, Z. Sun*. Study on the convergnce of plug-and-play ISTA with adaptive-kernel denoisers. IEEE Signal Processing Letters (IEEE-SPL), vol. 28, pp. 1918-1922, 2021.[pdf|code]

Visualization Results

Theories

...

...