Group-sparse Matrix Recovery
  We apply the OSCAR (octagonal selection and clustering algorithms for regression) in recovering group-sparse matrices (two-dimensional---2D---arrays) from compressive measurements. We propose a 2D version of OSCAR (2OSCAR) consisting of the $\ell_1$ norm and the pair-wise $\ell_{\infty}$ norm, which is convex but non-differentiable. We show that the proximity operator of 2OSCAR can be computed based on that of OSCAR. The 2OSCAR problem can thus be efficiently solved by state-of-the-art proximal splitting algorithms. Experiments on group-sparse 2D array recovery show that 2OSCAR regularization solved by the SpaRSA algorithm is the fastest choice, while the PADMM algorithm (with debiasing) yields the most accurate results. 
Xiangrong Zeng and M\'ario A. T. Figueiredo
cs.LG cs.CV stat.ML