A generalized form of the InSAR phase unwrapping problem based on a compressed sensing technique

This paper deals with the interferometric synthetic aperture radar (InSAR) phase unwrapping problem. The proposed appraoch is based on the relationship between the gradient vectors of the observed wrapped phase and the true phase respectively, when the Itoh condition is satisfied. Since this relationship is violated by the residu pixels in the observed wrapped phase, we propose, in this paper, a general problem formulation which takes into account the estimation error due to these residu values. The main idea is based on compressed sensing technique to estimate the true phase and the estimation error simultaneously. To obtain a sparsity representation of the unknown true phase image, we use the curvelet transform orthobasis dictionary and the error is assumed to be a sparse signal. Finally, the minimization of the result l₁ problem is insured by the Basis Pursuit algorithm (BP). The proposed unwrapping approach shows high performance when tested and validated with simulated and real interferograms and compared with two recent similar algorithms.