Structured Sparsity via Half-Quadratic Minimization

This paper proposes a general framework for the problem of structured sparsity via half-quadratic (HQ) minimization. Based on the theory of convex conjugacy, we firstly define an l(2,1)(epsilon)-norm and induce a family of penalty functions for structured sparsity. Then we build and discuss some important properties of these functions. By introducing the multiplicative auxiliary variable in HQ, we further reformulate the structured sparsity problem as an augmented half-quadratic optimization problem, and propose a general iteratively reweighted framework to alternately minimize the cost function. The proposed framework can be used in sparse representation, group sparse representation and multi-task joint sparse representation. Finally, in terms of the task of multi-biometric information fusion, we apply our proposed methods to obtain a novel fusion strategy, named structured fusion. Experimental results on the multi-biometric problems corroborate our claims and validate the proposed methods.