A two-term hybrid method with restart strategy for signal processing and image recovery

This paper presents a two-term hybrid conjugate gradient (CG) method with a restart strategy for solving large-scale nonlinear equations, particularly those arising in signal processing and image recovery. The proposed method generalizes four existing algorithms, thereby yielding a novel hybrid CG parameter that combines their desirable properties while ensuring sufficient descent and boundedness of the search direction. Furthermore, a restart mechanism is incorporated to accelerate convergence by adaptively resetting the search direction whenever progress slows. Under suitable assumptions, global convergence and convergence rate of the proposed method is established. Numerical experiments on benchmark problems demonstrate that the proposed method achieves faster convergence and higher solution accuracy than existing methods.