Consistent 2-D phase unwrapping guided by a quality map

The problem of 2D phase unwrapping arises when a spatially varying quantity is measured module some period. One needs to reconstruct a smooth unwrapped phase, consistent with the original data, by adding a multiple of the period to each sample. Smoothness typically cannot be enforced over all of the scene, due to noise and localized jumps. An unwrapping algorithm may form a mask within which phase discontinuities are allowed. In interferometry a quality map is available, indicating the reliability of the measurements. In this case, the mask should be contained as much as possible in areas of low quality. This paper presents an algorithm for phase unwrapping in which the mask design is guided by the quality map. The mask is grown from the residues (as defined by Goldstein et al.) into areas where the quality is below a threshold. A connected component of the mask stops growing when its residue charge becomes balanced. The threshold is raised as necessary to allow growth. This stage terminates when all components are balanced. The mask is then thinned by removing points that are not needed to cover the residues correctly. The unwrapped phase is found by simple 1D unwrapping along paths that avoid the mask. The authors present an example solution found by the algorithm and discuss possible modifications.