Optimization Theory: Concepts, Methods, and Applications

This work presents a new iterative scheme and establishes its convergence results to approximate the fixed points of nonexpansive mapping. In particular, we demonstrate effectiveness of our proposed iterative scheme in the image restoration process by formulating the problem as a split feasibility problem (SFP). A comparative analysis reveals that our scheme not only converges faster than some classical iterative processes but also achieves good restoration quality, thereby bridging the gap between abstract convergence results and real-world computational performance. The integration of fixed point methods with modern image restoration highlights the novelty of our approach and underscores its potential as a powerful tool for advancing variational and projection-based techniques in imaging sciences.