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Modern Synthetic Aperture Radar (SAR) missions provide an unprecedented massive interferometric SAR (InSAR) time series. The processing of the Big InSAR Data is challenging for long-term monitoring. Indeed, as most deformation phenomena develop slowly, a strategy of a processing scheme can be worked on reduced volume data sets. This paper introduces a novel ComSAR algorithm based on a compression technique for reducing computational efforts while maintaining the performance robustly. The algorithm divides the massive data into many mini-stacks and then compresses them. The compressed estimator is close to the theoretical Cramer–Rao lower bound under a realistic C-band Sentinel-1 decorrelation scenario. Both persistent and distributed scatterers (PSDS) are exploited in the ComSAR algorithm. The ComSAR performance is validated via simulation and application to Sentinel-1 data to map land subsidence of the salt mine Vauvert area, France. The proposed ComSAR yields consistently better performance when compared with the state-of-the-art PSDS technique. We make our PSDS and ComSAR algorithms as an open-source TomoSAR package. To make it more practical, we exploit other open-source projects so that people can apply our PSDS and ComSAR methods for an end-to-end processing chain. To our knowledge, TomoSAR is the first public domain tool available to jointly handle PS and DS targets.