Fixed-Point and Objective Convergence of Plug-and-Play Algorithms

A standard model for image reconstruction involves the minimization of a data-fidelity term along with regularizer, where optimization is performed using proximal algorithms such as ISTA and ADMM. In plug-and-play (PnP) regularization, operator (associated regularizer) in ADMM replaced by powerful denoiser. Although PnP regularization works surprisingly well practice, its theoretical convergence-whether convergence iterates guaranteed if they minimize some objective function-is not completely understood even simple linear denoisers nonlocal means. particular, while there are either iterate or established separately, simultaneous guarantee on available any denoiser to our knowledge. this paper, we establish both forms special class denoisers. Notably, unlike existing focus symmetric denoisers, analysis covers non-symmetric means almost convex data-fidelity. The novelty regard that make use theory averaged operators work inner product (and norm) derived from denoiser; latter requires us appropriately define gradient associated term. We validate results experiments.