An Improved Optimal Proximal Gradient Algorithm for Non-Blind Image Deblurring

TL;DR

This paper presents an improved proximal gradient algorithm for non-blind image deblurring that enhances image quality metrics like PSNR and SSIM by efficiently solving the optimization problem with regularization.

Contribution

The paper introduces IOptISTA, an improved optimal proximal gradient algorithm that leverages a weighting matrix for better performance in non-blind image deblurring.

Findings

Enhanced PSNR and SSIM compared to existing methods

Reduced tolerance in numerical experiments

Effective for $l_1$ and total variation regularization

Abstract

Image deblurring remains a central research area within image processing, critical for its role in enhancing image quality and facilitating clearer visual representations across diverse applications. This paper tackles the optimization problem of image deblurring, assuming a known blurring kernel. We introduce an improved optimal proximal gradient algorithm (IOptISTA), which builds upon the optimal gradient method and a weighting matrix, to efficiently address the non-blind image deblurring problem. Based on two regularization cases, namely the $l_1$ norm and total variation norm, we perform numerical experiments to assess the performance of our proposed algorithm. The results indicate that our algorithm yields enhanced PSNR and SSIM values, as well as a reduced tolerance, compared to existing methods.