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The synthesis of sparse antenna arrays has many practical applications in situations where the weight, size and cost of antennas are limited. In this communication the antenna array synthesis problem, with minimum number of elements, is studied from the new perspective of sparseness constrained optimization. The number of antenna elements in the array can be efficiently reduced by casting the array synthesis problem into the framework of sparseness constrained optimization and solving with the Bayesian compressive sensing (BCS) inversion algorithm. Numerical examples of both linear and planar arrays are presented to show the high efficiency of achieving the desired radiation pattern with a minimum number of antenna elements.