A new spectral conjugate gradient method for convex constrained monotone nonlinear equations with application to image restoration

In recent years, Spectral Conjugate Gradient (SCG) algorithms have gained increasing attention for image restoration problem. This study proposed a three efficient SCG method for solving convex-constrained nonlinear equations with image recovery. The proposed algorithms ensure bounded search directions that exhibit sufficient descent. Furthermore, the algorithm’s global and Q-linear convergence is established under a reasonable assumptions. To assess its effectiveness, we conduct numerical tests, comparing the proposed algorithms with existing methods. Finally, we apply the proposed method to image restoration problems.