Majorization–minimization generalized Krylov subspace methods for ℓp – ℓq optimization applied to image restoration

A new majorization–minimization framework for ℓp – ℓq image restoration is presented. The solution is sought in a generalized Krylov subspace that is build up during the solution process. Proof of convergence to a stationary point of the minimized ℓp – ℓq functional is provided for both convex and nonconvex problems. Computed examples illustrate that high-quality restorations can be determined with a modest number of iterations and that the storage requirement of the method is not very large. A comparison with related methods shows the competitiveness of the method proposed.