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This paper presents an efficient algorithm to solve total variation (TV)regularizations of images contaminated by a both blur and noise. Theunconstrained structure of the problem suggests that one can solve aconstrained optimization problem by transforming the original unconstrainedminimization problem to an equivalent constrained minimization one. Anaugmented Lagrangian method is developed to handle the constraints when themodel is given with matrix variables, and an alternating direction method (ADM)is used to iteratively find solutions. The solutions of some sub-problems arebelonging to subspaces generated by application of successive orthogonalprojections onto a class of generalized matrix Krylov subspaces of increasingdimension.

A generalized matrix Krylov subspace method for TV regularization