Phase unwrapping for interferometric synthetic aperture radar by use of Helmholtz equation eigenfunctions and the first Green’s identity

Abstract

We develop a new algorithm for interferometric synthetic aperture radar (SAR) phase unwrapping based on the first Green’s identity with the Green’s function representing a series in the eigenfunctions of the two-dimensional Helmholtz homogeneous differential equation. This provides closed-form solutions with use of one- or two-dimensional fast Fourier transforms. The algorithm is elaborated by using adaptive regularization of the interferometric phase gradient estimation. To diminish underestimation of the unwrapped phase typical of the linear phase unwrapping algorithms, the bias in the measured interferometric SAR phase is calculated in terms of the probability density function of the error in the processed interferometric SAR phase.