Approximation SR1-based algorithms for nonlinear image processing

Variational models of unconstrained optimization problems have been found in a variety of significant applications of research areas, such as image restoration. Among the QN methods, memoryless methods have been regarded effective techniques for solving large-scale problems that can be considered as one step limited memory QN methods. In this paper, we present an efficient memoryless symmetric rank-one (SR1) updating formula to compute meaningful solutions for large-scale problems arising in some image restoration problems. It is shown that the numerical experiments support the theoretical considerations for the usefulness of the proposed method. Meanwhile, comparisons on various well-known methods in the literature are presented to illustrate the effectiveness of the proposed method particularly for images of large size.