Selection of the regularization parameter in the P-LASSO for the noisy covariance model

In this paper, the Positive constrained Least Absolute Shrinkage and Selection Operator (P-LASSO) is studied for sparse support recovery using the correlation information in Compressive sensing (CS). A structural constraint is obtained for selecting the regularization parameter in the case of additive Gaussian noise. Since the measurements are finite in practice, the probability of successful recovering the sparse support is discussed. A lower bound of the probability is derived. Experimental results are provided to illustrate the validity of our main results.