Solving the Phase Unwrapping Problem by a Parametrized Network Optimization Approach

Abstract

The phase unwrapping problem consists in recovering a real function U defined on a discrete set (i.e. a rectangular grid) from the knowledge of its values modulus 2π. The phase unwrapping problem is the key problem in interferometry, for simplicity we restrict our attention to the SAR (Synthetic Aperture Radar) interferometry problem. The phase unwrapping problem is not well defined in fact it has infinitely many solutions, so that it must be “regularized” to be satisfactorily solvable. We propose a formulation of the phase unwrapping problem based on a network optimization problem depending on a parameter. We study the behaviour of the solution obtained as a function of this parameter. Numerical algorithms to solve the network optimization problems obtained are proposed. We report some numerical experience comparing the results obtained with the algorithm proposed here with the results obtained with another algorithm proposed in the scientific literature. The numerical experience proposed is relative to synthetic data and to real SAR interferometry data. The real data are taken from the ERS missions of the European Space Agency (ESA).