Perturbed reflected forward backward splitting algorithm for monotone inclusion

Abstract

In this paper, we investigate a new reflected forward–backward splitting algorithm with self-adaptive step sizes to solve monotone inclusion problems. The implementation of our algorithm does not require the knowledge of the Lipschitz constant for the Lipschitz continuous monotone operator, unlike existing reflected forward–backward splitting algorithms, which necessitate this information during implementation. The weak convergence theorem of the proposed algorithm is given under standard conditions. We compare numerically our algorithm with other related ones in the literature through its applications in signal processing and image deblurring.