Mixed norms with overlapping groups as signal priors

In a number of signal processing applications, problem formulations based on the 1 norm as a sparsity inducing signal prior lead to simple algorithms with good performance. However, 1 norm is not flexible enough to handle certain signal structures that are represented using a few groups of coefficients. Formulations that make use of mixed norms provide an alternative that can handle such signals by forcing sparsity on a group level and allowing non-sparse distributions within the groups. However, conventional mixed norms allow only non-overlapping groups – a restriction that leads to characteristics unlikely for natural signals. In this paper, we investigate mixed norms with overlapping groups. We consider a simple denoising formulation that gives a convex optimization problem and provide an algorithm that solves the problem. We use the algorithm to evaluate the performance of mixed norms with overlapping groups as signal priors.

• Type: Journal
• Year: 2011
• Where: ICASSP
• Authors: Ilker Bayram
• Keywords: Algorithm, Certain Signal Structures, ICASSP 2011, Mixed Norms, Signal Processing