A MAJORIZATION-MINIMIZATION GOLUB-KAHAN BIDIAGONALIZATION METHOD FOR?2-?q MIMIMIZATION WITH APPLICATIONS IN IMAGE RESTORIZATION

An image restorization problem is often modelled as a discrete ill posed problem. In general, its solution, even if it exists, is very sensitive to the perturbation in the data. Regularization methods reduces the sensitivity by replacing this problem with a minimization problem with a fidelity term and lq regularization term. In order to improve the sparsity of the solution, we only consider the case of 0 < q <= 1 in this paper. This paper presents a majorization-minimization Golub-Kahan bidiagonalization algorithm to solve this kind of minimization problems. The solution subspace is extended by the Golub-Kahan bidiagonalization process. The restarted case is also considered. The regularization parameter is determined by using the discrepancy principle. Several examples in image restorization are shown for the proposed methods.