  Interferometric phase linking (IPL) has become a prominent technique for
processing images of areas containing distributed scaterrers 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 of pixel patches on a sliding window. This paper reformulates
this task as a covariance fitting problem: in this setup, IPL appears as a form
of projection of an input covariance matrix so that it satisfies the phase
closure property. Given this modular formulation, we propose an overview of
covariance matrix estimates, regularization options, and matrix distances, that
can be of interest when processing multi-temporal SAR data. In particular, we
will observe that most of the existing IPL algorithms appear as special
instances of this framework. We then present tools to efficiently solve related
optimization problems on the torus of phase-only complex vectors:
majorization-minimization and Riemannian optimization. We conclude by
illustrating the merits of different options on a real-world case study.
