Optimizing Conjugate Gradient Directions for Image Deblurring in Compressed Sensing: A Hybridized Approach.

Hybridization emerges as a promising strategy for refining conjugate gradient (CG) directions, pivotal in tackling image deblurring within compressed sensing frameworks. This abstract introduces a novel hybrid CG parameterization, surpassing the recent SGCS algorithm (Auwal et al., 2020). The method integrates a convex combination approach, dynamically updating the combination parameter (µk) via the Dai and Liao conjugacy condition. Additionally, a derivative-free line search efficiently determines optimal step lengths (αk). With a focus on satisfying sufficient descent conditions, imperative for global convergence, the method demonstrates superior performance through numerical experiments compared to existing approaches. Furthermore, the extension of this method to ℓ1- norm regularized problems enhances its efficacy in restoring blurred images within compressed sensing contexts. [ABSTRACT FROM AUTHOR]