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 article 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. This 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 detail. The simulation results reveal that the proposed method can efficiently synthesize a sparse array within a significantly shorter time in comparison to the state-of-the-art techniques. As a result, it can be applied to generate arrays with large apertures. In addition, both numerical and experimental results demonstrate that the synthesized sparse array offers superior image quality when compared with both state-of-the-art and commonly used sparse arrays with an equivalent number of antenna elements.