Regularized Focuss for Subset Selection in Noise

This paper considers subset selection in the presence of noise via algorithms that minimize diversity measures. This leads to iterative procedures like regularized FOCUSS in which each iteration involves the solution to a regularized least squares problem. Several di erent methods for choosing the regularization parameter such as the discrepancy principle and the L-curve technique are evaluated for this purpose and compared. To overcome some of the limitations in existing methods, a modi ed L-curve approach is proposed. Experiments using regularized FOCUSS with the di erent methods for choosing the regularization parameter are conducted and compared with a sequential subset selection method, the Orthogonal Matching Pursuit (OMP) method. Results show that a modi ed L-curve approach works well for nding the regularization parameter in this application.