Two descent spectral conjugate gradient techniques with practical application for image restoration

In an attempt to modify the well-known Polak-Ribière-Polyak technique, Jiang et al. introduced a descent nonlinear conjugate gradient algorithm that uses a restart condition to guarantee the global convergence. Here, according to their study, we develop two descent spectral conjugate gradient techniques which, regardless of the line search, fulfill the sufficient descent condition. We analyze convergence of the methods as well. Numerical implementations on a collection of the CUTEr functions as well as the image restoration cases are done which show that the proposed methods are promising.