This paper presents a new SAR ground moving target imaging (GM-TIm) algorithm based on an unified framework of Keystone transformation (KT). To combat the inherent range-azimuth coupling, an tandem two-step strategy is designed, where the range decoupling is implemented by polar format algorithm (PFA) and the azimuth decoupling is finished by an novel time-frequency representation method that is Lv's distribution (LVD). We show, mathematically, that the azimuth resampling of PFA has inherently the same mechanism as the KT, and also, the LVD achieves the optimal performance when it is performed in accordance with the KT principle. Therefore, multiple moving targets can be imaged simultaneously. Focused targets' responses can be obtained in both range and azimuth dimensions. Isotropic point target simulation is designed, and experiments are carried out to validate our proposed SAR-GMTIm algorithm.