A reduced l2-l1 model with an alternating minimisation algorithm for support recovery of multiple measurement vectors

The authors address the problem of support recovery with multiple measurement vectors (MMV) in this study. The scale of an MMV is reduced by using the singular value decomposition technique, and a novel l₂-l₁ minimisation model with two variables for the reduced MMV is proposed. Then a new alternating minimisation algorithm based on the alternating direction method of multipliers is presented. They prove the globally convergence property of the presented algorithm. Several numerical simulations both on random data and for direction-of-arrival estimation are conducted to evaluate the performance of the proposed method for support recovery of MMV.