Sparse Two-Dimensional Phase Unwrapping Using Regular-Grid Methods

Phase unwrapping is usually defined as the reconstruction of a function sampled on a spatial grid given its value modulo 2 pi. Phase unwrapping is a key step in image reconstruction in many imaging techniques including interferometric synthetic aperture radar (InSAR). In recent years, many new methods have been developed to exploit the presence of coherent or persistent scattering points for extracting deformation signatures in regions where the conventional InSAR fails. These techniques often yield measurements that are only poorly sampled spatially, yet these sparse data must still be unwrapped if we are to be able to extract useful geophysical information. The conventional well-sampled 2-D phase unwrapping problem based on phase residues is fairly well understood, and many novel techniques involving geometry and network flow concepts have been implemented successfully to date. For sparse data, residues may be computed over the Delaunay triangulation of the data points, but published algorithms meet with limited success when the sparse data are unwrapped. The advantages of modern unwrapping methods applicable to well-sampled data are often lost when sparse data are analyzed. In this letter, we show that a nearest neighbor interpolation scheme allows powerful and existing 2-D solvers to be applied to sparse data. We present results using both simulated and real data sets to illustrate our method.