Coherence Matrix Estimation with Total Positivity Regularization for Interferometric Phase Linking

Interferometric phase linking has become a critical step in distributed scatterer (DS) interferometry, yet its performance is significantly affected by inaccuracies in the coherence matrix and its inverse, such as the precision matrix. Recent studies have attempted to address this issue using regularization techniques, modifying diagonal elements or shrinking the coherence matrix towards the identity matrix. However, these methods do not sufficiently resolve the problem. In this article, we propose a novel regularized coherence matrix estimation approach to enhance interferometric phase linking. Specifically, we introduce a coherence matrix estimator based on maximum likelihood estimation, constrained by the multivariate totally positive of order 2 ($ \rm{MTP}_{2}$), also called total positivity. A coordinate-descent algorithm is then applied to efficiently estimate both the coherence and precision matrices. Simulation experiments validate the effectiveness of the proposed approach, particularly in precision matrix estimation. Furthermore, real data experiments conducted at Chengdu Tianfu International Airport and Chongqing Jiangbei International Airport demonstrate that our approach outperforms three state-of-the-art coherence matrix regularization techniques.