Improving Atmospheric Phase Screen (APS) Removal in Multi-temporal Radar Interferometry through Complex Interpolation

Many applications of synthetic aperture radar differential interferometry (DInSAR) lead to a set of sparse phase measurements, e.g. in the processing of long multitemporal stacks of SAR differential interferograms through persistent scatterers interferometry (PSI) techniques. Often, sparse phase data have to be unwrapped, and then interpolated on a regular grid to be useful for subsequent processing steps. This step is necessary for instance in the reconstruction of the so-called APS (Atmospheric Phase Screen). Atmospheric artifacts superimposed on DInSAR measurements have the potential of hindering the accurate estimation of deformation signals. Indeed, sometimes the spatial frequencies of the atmospheric phase contributions can overlap those of deformation signals, so that such artifacts can be misinterpreted as deformation features. For the phase unwrapping stage, the solutions are directly dependent on the PS network density; moreover, phase aliasing, which appears when the signal sampling does not satisfy the Nyquist condition, especially in presence of noise, increases when passing from regular-grid to sparse data. This is because the phase sampling conditions get usually worse. An improvement of the APS estimation step has been proposed, by investigating 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, the proposed 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 smooth phase field 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 a smoother absolute phase field. The performances of this empirical approach are evaluated here over a real dataset, that is composed by 30 ascending SAR X-band COSMO-SkyMed images. The images cover the urban area and outskirts of the capital of Haiti, Port-au-Prince. The accuracy of the reconstructed phase fields is analyzed by the local value of the final inter-image phase coherence (?int), a quality figure related to the residual phase noise after subtraction of all modeled contributions. Its values are taken on points (PS) not used in the interpolation, using different spatial densities and random subsampling patterns in a test area characterized by a strong subsidence bowl. The obtained results may be applied into a broader context than the one specific to the PSI technique, considering the few assumptions on the initial phase field, i.e. its smoothness and good sampling conditions.