DOI: 10.24193/fpt-ro.2025.2.01

Authors: A. Adamu, P. Kumam, D. Kitkuan, P. Yodjai and K. Sitthithakerngkiet

Abstract: Following Chidume (Contemp. Math. (Amer. Math. Soc.) 659,31-41, 2016) who posed an interesting question concerning the proximal point algorithm "Can an iteration process be developed which will not involve the computation of (I+λ_n A)^-1x_n at each step of the iteration process and which will guarantee strong convergence to a solution of 0 ∈ Au?", in this paper, we provide an affirmative answer to the question above concerning the forward-backward algorithm. We introduce a resolvent computational-free alternative of the forward-backward algorithm for approximating zeros of sum of two monotone operators and prove a strong convergence theorem in the setting of real Hilbert spaces. Furthermore, we use our algorithm in the restoration process of some degraded images and sparse signals. In addition, numerical illustrations of our proposed algorithm in L₂([0,1]) is also presented. Finally, numerical comparison of the performance of our new method with some classical methods in the literature are presented.

Key Words and Phrases: Monotone, convex minimization, image restoration, signal recovery.

2010 Mathematics Subject Classification: 47H20, 49M20, 49M25, 49M27, 47J25, 47H05, 47H10.

Published on-line: May 1st, 2025.

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