In micro-motion signal processing, incomplete and phase-corrupted radar echoes result in bad time-frequency representation and thus prevent the extraction of micro-motion features. To solve the problem, the optimization model is developed to reconstruct phase-corrupted and incomplete m-D signals. The optimization model is solved through an alternating iteration algorithm. In each iteration, the recovery signal and the phase error are updated by the alternating direction method of multipliers and the least-squares theory, respectively. For m-D signal real-time processing to save radar time resources, the received signal can be directly sparse recovered real-rather than waiting for the complete signal. Additionally, the statistics of patch offsets are applied to construct the termination condition. Finally, the effectiveness of the proposed method is validated from the simulation results.