Aliasing in InSAR 2-D Phase Unwrapping and Time Series
Karissa Pepin, H. A. Zebker
Abstract
We quantify and characterize an often-overlooked error source in InSAR and derived time series: aliasing from insufficiently sampled interferograms in space and time. Conditions that lead to unrecoverable aliasing, namely, when true phase gradients greater than π rad per pixel form a closed loop, result in a biased loss in unwrapped phase magnitude that is proportional to the number of high-gradient (> π) loops encircling a pixel. High-gradient interferogram loops are influenced by the radar system wavelength, its spatial resolution, imaging geometry, and the local noise level. Furthermore, spatial filtering may induce further aliasing because it decreases the spatial resolution and, consequently, the physical gradient tolerance. We show here that beyond aliasing in a single interferogram, there follows a similar loss in time series, which we demonstrate with small-baseline subset (SBAS) techniques. We find that aliasing has an intimate relationship with the time between image acquisitions as the displacement field evolves; consequently, aliasing errors often increase with increasing temporal baseline, and we observe a systematic decrease in SBAS solution magnitudes and a spatiotemporal distortion of displacement patterns with increasing maximum temporal baseline. Sentinel-1 observations of three study areas (Kilauea Volcano, the Delaware Basin, and California’s Central Valley) show that some of the best time series solutions with respect to ground-truth include long-temporal baseline interferograms and others require their explicit exclusion, suggesting there is a delicate balance between aliasing and noise reduction that not only varies between study areas, but may even be unique to each pixel.