The Trimmed LASSO for Direction of Arrival Estimation by the Generalized Soft-Min Penalty

The trimmed lasso is a new nonconvex regularized approach for sparse signal recovery, which shows better estimation results in the single measurement vector problem. In this paper, we define the penalty term of the trimmed lasso in the multiple measurement vector model by £
2,1
-norm. We then present an approach to apply the trimmed lasso to on-grid based direction-of-arrival estimation problems by the alternating directions method of multipliers (ADMM) and majorization-minimization algorithm, which change the nonconvex objective to the convex weighted problem. Numerical simulations show that the proposed method improves the performance over £2,1 minimization algorithm.