Cross-Products LASSO

Negative co-occurrence is a common phenomenon in many signal processing applications. In some cases the signals involved are sparse, and this information can be exploited to recover them. In this paper, we present a sparse learning approach that explicitly takes into account negative co-occurrence. This is achieved by adding a novel penalty term to the LASSO cost function based on the cross-products between the reconstruction coefficients. Although the resulting optimization problem is non-convex, we develop a new and efficient method for solving it based on successive convex approximations. Results on synthetic data, for both complete and overcomplete dictionaries, are provided to validate the proposed approach.