A General Formulation for Redundant Integration of Finite Differences and Phase Unwrapping on a Sparse Multidimensional Domain

Phase unwrapping and integration of finite differences are key problems in several technical fields, among which is synthetic aperture radar (SAR) interferometry. In this paper, we propose a general formulation for robust and efficient integration of finite differences and for phase unwrapping, which includes standard techniques (e.g., minimum cost flow and least squares phase unwrapping) as subcases. The proposed approach allows obtaining more reliable and accurate solutions by exploiting redundant differential estimates (not only between nearest neighboring points) and multidimensional information (e.g., multitemporal). In addition, a model of the signal (e.g., multibaseline or multifrequency) or external data (e.g., GPS or leveling measurements) can be integrated. The method requires the solution of linear or quadratic programming problems, for which computationally efficient algorithms exist. The validation tests performed on real and simulated SAR data confirm the validity of the method, which was integrated in our production chain and successfully used also in massive productions.