Covariance Fitting Interferometric Phase Linking: Modular Framework and Optimization Algorithms

Abstract

Interferometric phase linking (IPL) has become a prominent technique for processing images of areas containing distributed scatterers in SAR interferometry. Traditionally, IPL consists in estimating consistent phase differences between all pairs of SAR images in a time series from the sample covariance matrix (SCM) of pixel patches on a sliding window. This article reformulates this task as a covariance fitting problem; IPL appears then as a form of projection of an input covariance matrix so that it satisfies the phase closure property. This approach yields a systematic methodology to frame IPL as an optimization problem on the torus of phase-only complex vectors. On the modeling side, the formulation is modular and allows for a flexible choice of covariance matrix estimates, regularization options, and matrix distances. In particular, we demonstrate that most existing IPL algorithms appear as special instances of this framework. In addition, we propose some new options, which were not covered by the state of the art, whose merits are illustrated through simulations and a real-world case study. On the computational side, another contribution of this article is the derivation of generic and computationally efficient algorithms for IPL using majorization-minimization (MM) and Riemannian optimization.