A Memory Gradient algorithm for ℓ2 — ℓ0 regularization with applications to image restoration

In this paper, we consider a class of differentiable criteria for sparse image recovery problems. The regularization is applied to a linear transform of the target image. As special cases, it includes edge preserving measures or frame analysis potentials. As shown by our asymptotic results, the considered ℓ₂ - ℓ₀ penalties may be employed to approximate solutions to ℓ₀ penalized optimization problems. One of the advantages of the approach is that it allows us to derive an efficient Majorize-Minimize Memory Gradient algorithm. The fast convergence properties of the proposed optimization algorithm are illustrated through image restoration examples.