Weighted covariance matching based square root LASSO

We propose a method for high dimensional sparse estimation in the multiple measurement vector case. The method is based on the covariance matching technique and with a sparse penalty along the ideas of the square-root LASSO (sr-LASSO). The method not only benefits from the strong characteristics of sr-LASSO (independence of the hyper-parameter selection from the noise variance), but also offers a performance near maximum likelihood. It performs close to the Cramer-Rao bound even at low signal to noise ratios and it is generalized to manage correlated noise. The only assumption in this matter is that the noise covariance matrix structure is known. The numerical simulation provided in an array processing application illustrates the potential of the method.