A novel double inertial viscosity algorithm for convex bilevel optimization problems applied to image restoration problems

Convex bilevel optimization holds a crucial role in the decision-making process in a hierarchical setting, while image restoration plays a critical role in signal processing and computer vision. In this paper, a new double inertial viscosity approximation method with a linesearch technique is introduced for solving convex bilevel optimization problems and then its strong convergence is analyzed under moderate conditions. As an application, our proposed algorithm is employed for solving image restoration problems. The experiment results highlight the specific advantages and potential infect of the algorithm over the existing algorithms in the literature, particularly in the domain of image restoration.