Homotopy algorithm using dichotomous coordinate descent iterations for sparse recovery

We propose a computationally efficient technique for recovery of sparse signals, which is based on dichotomous coordinate descent iterations, homotopy, and reweighting. We derive optimal rules for adding and removing elements to/from the support, guaranteeing that the cost function is minimized. Numerical examples show that the proposed technique achieves a mean-squared error smaller than that of the YALL1 algorithm and complexity comparable to that of the matched pursuit algorithm.