An innovative inertial extra-proximal gradient algorithm for solving convex optimization problems with application to image and signal processing

This study introduces an innovative approach to address convex optimization problems, with a specific focus on applications in image and signal processing. The research aims to develop a self-adaptive extra proximal algorithm that incorporates an inertial term to effectively tackle challenges in convex optimization. The study's significance lies in its contribution to advancing optimization techniques in the realm of image deblurring and signal reconstruction. The proposed methodology involves creating a novel self-adaptive extra proximal algorithm, analyzing its convergence rigorously to ensure reliability and effectiveness. Numerical examples, including image deblurring and signal reconstruction tasks using only 10% of the original signal, illustrate the practical applicability and advantages of the algorithm. By introducing an inertial term within the extra proximal framework, the algorithm demonstrates potential for faster convergence and improved optimization outcomes, addressing real-world challenges of image enhancement and signal reconstruction. The algorithm's incorporation of an inertial term showcases its potential for faster convergence and improved optimization outcomes. This research significantly contributes to the field of optimization techniques, particularly in the context of image and signal processing applications.