Integrability-regularized phase unwrapping via sparse error correction

We propose a new formulation of the classical two-dimensional phase unwrapping problem. Using a sparse-error, gradient-domain measurement model, we simultaneously seek the absolute phase and sparse gradient errors that minimize a novel energy functional that strongly encourages the integrability of the corrected gradient field. Our approach can be cast as a generalized lasso problem, and we compute the solution using the alternating direction method of multipliers (ADMM) algorithm. Adopting a commonly-used inter-ferometric synthetic aperture radar noise model, we evaluate our technique for several synthetic surfaces.