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In the area of near-field millimeter-wave imaging, the generalized sparse array synthesis (SAS) method is in great demand. The traditional methods usually employ the greedy algorithms, which may have the convergence problem. This paper proposes a convex optimization model for the multiple-input multiple-output (MIMO) array design based on the compressive sensing (CS) approach. We generate a block shaped reference pattern, to be used as an optimizing target. The pattern occupies the entire imaging area of interest in order to involve the effect of each pixel into the optimization model. In MIMO scenarios, we can fix the transmit subarray and synthesize the receive subarray, and vice versa, or doing the synthesis sequentially. The problems associated with focusing, sidelobes suppression, and grating lobes suppression of the synthesized array are examined in details. Numerical and experimental results demonstrate that the synthesized sparse array can offer better image qualities than the sparse arrays with equally spaced or randomly spaced antennas with the same number of antenna elements.