Quality Coefficients for Interferometric Phase Linking
Magnus Heimpel, Irena Hajnsek, Othmar Frey
TL;DR
This work introduces a unified theoretical framework for interferometric phase linking in distributed scatterer InSAR and defines three normalized quality coefficients: the closure phase coefficient $\gamma_{CP}$, the method-specific goodness-of-fit coefficient $\gamma_{GOF}$, and the ambiguity coefficient $\gamma_A$. The coefficients are computed from the coherence matrix and phase-linking solutions across eigendecomposition and phase triangulation methods, with noise-floor corrections and normalization to [0,1], enabling consistent cross-stack thresholding. Experiments on TerraSAR-X data over Visp validate that $\gamma_{CP}$ effectively pre-screens stable areas, $\gamma_{GOF}$ aligns with established indicators while generalizing them, and $\gamma_A$ flags unstable yet well-fitting solutions, collectively supporting robust pixel selection and quality control in DS-InSAR processing. The framework unifies existing phase-linking criteria, clarifies their connections to objective functions, and provides practical tools for improved deformation mapping in challenging decorrelated regions.
Abstract
In multi-temporal InSAR, phase linking refers to the estimation of a single-reference interferometric phase history from the information contained in the coherence matrix of a distributed scatterer. Since the phase information in the coherence matrix is typically inconsistent, the extent to which the estimated phase history captures it must be assessed to exclude unreliable pixels from further processing. We introduce three quality criteria in the form of coefficients, for threshold-based pixel selection: a coefficient based on closure phase that quantifies the internal consistency of the phase information in the coherence matrix; a goodness-of-fit coefficient that quantifies how well a resulting phase history estimate approximates the phase information according to the characteristic optimization model of a given phase linking method; and an ambiguity coefficient that compares the goodness of fit of the original estimate with that of an orthogonal alternative. We formulate the phase linking methods and these criteria within a unified mathematical framework and discuss computational and algorithmic aspects. Unlike existing goodness-of-fit indicators, the proposed coefficients are normalized to the unit interval with explicit noise-floor correction, improving interpretability across stacks of different size. Experiments on TerraSAR-X data over Visp, Switzerland, indicate that the closure phase coefficient effectively pre-screens stable areas, the goodness-of-fit coefficient aligns with and systematically generalizes established quality indicators, and the ambiguity coefficient flags solutions that fit well but are unstable. Together, the coefficients enable systematic pixel selection and quality control in the interferometric processing of distributed scatterers.