On convex combinations of norms for group sparsity

Abstract

Formulations based on the l 1 norm are widely used for the restoration and/or reconstruction of ‘sparse’ signals. However, the l 1 norm does not provide a rich enough model for signals that are not only sparse but also host more complex structures. Based on this observation, we investigate convex combinations of l 1 and l 2 norms. Employing a simple denoising formulation, we provide a geometric interpretation for the solution of the problem. We hope that this interpretation sheds light on formulations based on norms of the mentioned kind.