On convex combinations of norms for group sparsity

Formulations based on the ℓ₁ norm are widely used for the restoration and/or reconstruction of `sparse´ signals. However, the ℓ₁ 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 ℓ₁ and ℓ₂ 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.