A Barzilai-Borwein gradient projection method for sparse signal and blurred image restoration

Abstract

We present a Barzilai-Borwein gradient method using the hyperplane projection technique of Solodov and Svaiter (1998) for solving the non-smooth nonlinear monotone equation arising from the reformulation of the ℓ1-norm regularized problem. The proposed method is an extension of the modified method by Liu and Duan (J. Inequal. Appl. 2015(1), 8, 2015) for solving signal and image restoration problems. The method is derivative-free and its search direction satisfies the sufficient descent condition. Numerical experiments presented show that the proposed method can recover sparse signals in fewer iterations and less CPU time and can reconstruct blurred images with higher quality compared to similar methods in the literature.