A Halpern Method for Solving Perturbed Double Inertial Krasnoselskii-Mann Iterations with Applications to Image Restoration Problems

In this paper, we introduce and study a Halpern inertial method for solving the general perturbed Krasnoselskii-Mann type algorithm in Hilbert space settings, where the underlying mapping is quasi-nonexpansive. We discuss convergence analysis of the method under some mild assumptions on the control sequences. We additionally present a numerical example to demonstrate the effectiveness of the method. Finally, we apply the method in solving image restoration problems. We evaluate the quality of the improvement in the Signal-to-Noise Ratio (ISNR) and the restored images using the Structural Similarity Index Measure (SSIM) metrics. The results of this work generalize and expand upon numerous results found in the literature.