Sparsity Within and Across Overlapping Groups

TL;DR

This paper introduces a generalized sparsity penalty that captures complex dependencies within and across groups, addressing computational challenges and demonstrating its application in inverse problem energy minimization.

Contribution

It proposes a novel generalized penalty for structured sparsity that encodes intricate intra- and inter-group dependencies, overcoming thresholding difficulties.

Findings

Modified penalty enables energy minimization in inverse problems

Demonstrates practical application in signal processing tasks

Addresses computational challenges of complex sparsity penalties

Abstract

Recently, penalties promoting signals that are sparse within and across groups have been proposed. In this letter, we propose a generalization that allows to encode more intricate dependencies within groups. However, this complicates the realization of the threshold function associated with the penalty, which hinders the use of the penalty in energy minimization. We discuss how to sidestep this problem, and demonstrate the use of the modified penalty in an energy minimization formulation for an inverse problem.