Split monotone variational inclusion with errors for image-feature extraction with multiple-image blends problem

Abstract

Abstract In this paper, we introduce a new iterative forward–backward splitting algorithm with errors for solving the split monotone variational inclusion problem of the sum of two monotone operators in real Hilbert spaces. We suggest and analyze this method under some mild appropriate conditions imposed on the parameters such that another strong convergence theorem for this problem is obtained. We also apply our main result to image-feature extraction with the multiple-image blends problem, the split minimization problem, and the convex minimization problem, and provide numerical experiments to illustrate the convergence behavior and show the effectiveness of the sequence constructed by the inertial technique.

Keywords

• Split monotone variational inclusion problem
• Convex minimization problem
• Maximal monotone operator
• Forward–backward method
• Iterative shrinkage thresholding
• Image-feature extraction