TSO-PL: A Novel Phase Linking Method for DS InSAR Based on a Two-Step Strategy to Optimize the Sample Coherence Matrix

Distributed scatterer interferometric synthetic aperture radar (DS InSAR) is a widely used technique for monitoring surface deformation, but its effectiveness is often compromised by temporal and spatial decorrelation, leading to degraded interferometric phase quality. Enhancing phase quality through phase linking (PL) is essential. However, existing PL methods struggle to produce high-quality sample coherence matrices (SCMs) due to the inhomogeneity and limited availability of low-coherence homogeneous samples. Consequently, accurately deriving phase matrices, sample coherence magnitude matrices (SCMMs), and precision matrices becomes challenging, significantly impacting the accuracy of PL estimation. To address these limitations, a two-step optimization-based PL (TSO-PL) method is proposed. TSO-PL integrates both the complex and real domain characteristics of the SCM and features two key innovations: 1) feature compression of the SCM (FC-SCM) to improve the signal-to-noise ratio of the phase and the accuracy of the coherence value in SCM and 2) adaptive nonlinear shrinkage of the SCMM (ANS-SCMM) to yield a more accurate SCMM by improving its structure. The simulation results demonstrate that TSO-PL is robust to variations in the estimation window size and homogeneous sample number, outperforming the phase triangulation algorithm (PTA), eigenvalue decomposition (EVD), and eigendecomposition-based maximum likelihood (EMI) methods in terms of accuracy and noise reduction. In a case study, TSO-PL improved the maximum deformation rate detection by 29.5%, 36.7%, and 31.1% compared with PTA, EVD, and EMI, respectively, with a significantly lower root mean square error (RMSE) of 11.3 mm. These findings demonstrate that TSO-PL effectively reduces phase noise, preserves fringe integrity, and enhances the identification of high-density monitoring points, leading to more accurate surface deformation assessments.