Optimization constraints and Practical Implementations of a Stochastic Primal-Dual Fixed-Point Algorithm for Blind Image Deconvolution

Abstract

Blind deconvolution problems present significant challenges primarily due to the uncertainty surrounding the blurring kernel. In this paper, we introduce the Stochastic Primal-Dual Fixed-Point (SPDFP) method as a solution to these difficulties. We establish its almost-sure convergence by utilizing strong convexity along with standard assumptions regarding the gradient of $ f_1(X, H) $, drawing inspiration from the work of [35]. Additionally, we showcase the application of SPDFP in image deblurring and also super-resolution, emphasizing its effectiveness and versatility in real-world contexts. This underscores the substantial potential of SPDFP to enhance performance in complex data scenarios.