|Abstract:An algorithm combining frequency domain imaging algorithm and compressed sensing （CS） framework is proposed in here for millimeter-wave multi-static sparse array imaging. The algorithm consists of two major steps. Firstly, the typical fast Fourier transform （FFT） algorithm used in square boundary array with phase center approximation （PCA） is carried out. However, the residual phase error introduced by the PCA at close range cannot be compensated completely, so in the second step, the modified sparse learning via iterative minimization （SLIM） algorithm which is in the CS framework is introduced to refocus the initial images. By combining PCA and the modified SLIM algorithm, the proposed algorithm reaches a better computational efficiency, improves the image quality, and alleviates the requirement for iterations of the original SLIM algorithm. Simulation results verify the effectiveness of this algorithm.