Krylov subspace split Bregman methods

Split Bregman methods are popular iterative methods for the solution of large-scale minimization problems that arise in image restoration and basis pursuit. This paper investigates the possibility of projecting large-scale problems into a Krylov subspace of fairly small dimension and solving the minimization problem in the latter subspace by a split Bregman algorithm. We are concerned with the restoration of images that have been contaminated by blur and Gaussian or impulse noise. Computed examples illustrate that the projected split Bregman methods described are fast and give computed solutions of high quality.