Efficient Iteratively Reweighted LASSO Algorithm for Cross-Products Penalized Sparse Solutions

In this paper, we describe an efficient iterative algorithm for finding sparse solutions to a linear system. Apart from the well-known L-1 norm regularization, we introduce an additional cost term promoting solutions without too-close activations. This additional term, which is expressed as a sum of cross-products of absolute values, makes the problem non-convex and difficult to solve. However, the application of the successive convex approximations approach allows us to obtain an efficient algorithm consisting in the solution of a sequence of iteratively reweighted LASSO problems. Numerical simulations on randomly generated waveforms and ECG signals show the good performance of the proposed method.