A fast algorithm for constrained GLAD estimation with application to image restoration

In order to relax need of the optimal regularization parameter to be estimated, a cooperative recurrent neural network (CRNN) algorithm for image restoration was presented by solving a generalized least absolute deviation (GLAD) problem. This paper proposes a fast algorithm for solving a constrained l₁-norm problem which contains the GLAD problem as its special case. The proposed iterative algorithm is guaranteed to converge globally to an optimal estimate under a fixed step length. Compared with the CRNN algorithm being continuous time, the proposed iterative algorithm has a fast convergence speed. Illustrative examples with application to image restoration show that the proposed iterative algorithm has a much faster convergence rate than the CRNN algorithm.