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As an effective method in signal reconstruction model, compressed sensing (CS) has achieved excellent performance in sparse array reconstruction. However, it is necessary to set the penalization factor before iterative calculation, which will increase the difficulty to convergence the result to the global optimal solution. In this paper, we remove the process of choosing penalization factor and reconstruction error by modifying the iterative expression as well as alternating direction method of multipliers (ADMM) algorithm respectively. In addition, the improved model is shown to be convex and thus can be solved using the CVX toolbox. Simulation result shows that the reference pattern could be reconstructed with minimum number of antenna elements by the proposed algorithms. Moreover, the proposed methods have significant performance improvement in main sidelobe level (MSL).
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