  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.
