Sparse synthetic aperture radar (SAR) imaging has emerged as a reliable microwave imaging scheme in the recent decade and excels in down-sampling reconstruction and full-sampling performance improvements such as noise, sidelobe, speckle, and ambiguity suppression. To utilize complex image products of sparse reconstruction for improvement in polarimetric, interferometric, and tomographic SAR imaging, it is necessary to evaluate the phase preservation of sparse SAR imaging. In this study, we first introduce the general alternating direction method of multipliers (ADMM) as the universal framework for sparse reconstruction algorithms and adopt chirp scaling algorithm (CSA)-based azimuth-range decouple operators to avoid expensive data storage and processing. Further, we theoretically analyze the phase preservation of the sparse reconstruction algorithm through a comparison with the reconstruction results of CSA. Finally, we conduct the interferometric offset test on the sparse reconstruction results of simulated and real Gaofen-3 (GF-3) SAR data, demonstrating the phase-preserving ability of sparse methods.