Interferometric Synthetic Aperture Radar (InSAR) phase unwrapping error is a major limiting factor on the InSAR-derived tectonic deformation velocity. This is particularly the case when atmospheric turbulence, large deformation gradient and strong phase noise exist. To address limitations of existing phase unwrapping error correction methods which are not supported for multi-looked InSAR data, here we present a new algorithm that integrates decorrelation phase correction, triplet phase closure (TPC) test and integer linear programming (ILP) to overcome this limit. The rationale behind is that we mitigate the phase inconsistence using decorrelation correction and then detect the phase unwrapping error magnitude using TPC. Next we borrow the ILP from Compressed Sensing that converts the phase unwrapping error correction to a sparse signal recovery problem. We demonstrated the validity of our method by using synthetic data and 5-years Sentinel-1 real data covering the Central San Andreas Fault creep section, where exists obvious tectonic deformation, strong atmospheric disturbance and decorrelated scatterers, and the inverted long-term creep model constrained by InSAR velocity after correction shows a lower uncertainty than that constrained by the uncorrected one.