On the interpolation of sparse-grid InSAR data without need of phase unwrapping

Sparse phase measurements often need to be interpolated on regular grids, to extend the information to unsampled locations. Typical cases involve the removal of atmospheric phase screen information from Interferometric Synthetic Aperture Radar (InSAR) stacks, or the retrieval of displacement information over extended areas in Persistent Scatterers Interferometry (PSI) applications, when sufficient point densities are available. This operation is usually done after a phase unwrapping (PU) of the sparse measurements to remove the sharp phase discontinuities due to the wrap operation. PU is a difficult and error-prone operation, especially for sparse data. In this work, we investigate from the empirical point of view an alternative procedure, which involves an interpolation of the complex field derived from the sparse phase measurements. Unlike traditional approaches, our method allows to bypass the PU step and obtain a regular-grid complex field from which a wrapped phase field can be extracted. Under general conditions, this can be shown to be a good approximation of the original phase without noise. Moreover, the interpolated, wrapped phase field can be fed to state-of-the-art, regular-grid PU algorithms, to obtain an improved absolute phase field, compared to the canonical method consisting of first unwrapping the sparse-grid data. We evaluate the performance of the method in simulation, comparing it to the classical methodology described above, as well as to an alternative procedure, recently proposed, to reduce a sparse PU problem to a regular-grid one, through a nearest-neighbor interpolation step. Results confirm the increased robustness of the proposed method with respect to the effects of noise and undersampling.