New Math Method Makes Medical and Satellite Images Much Sharper

Phase unwrapping is a key step in interferometric and coherent imaging, where the physical quantity of interest is carried by a phase that the instrument delivers only modulo 2π. In two dimensions, the hard part is telling apart the jumps caused by wrapping from those produced by noise, true discontinuities, under-sampling or decorrelation. Spatial-domain and frequency-domain methods have both been studied extensively, each with advantages the other lacks, but hybrid schemes combining the two remain scarce.

Antoine Moevus and Max Mignotte propose a semi-global tile-based strategy in which every tile is unwrapped in the frequency domain, through the Discrete Cosine Transform (DCT) and the least squares (LS) formalism of Ghiglia et al., with the tiles merged spatially. Unwrapping and noise filtering are performed jointly, which regularizes an otherwise ill-posed inverse problem. An error stays confined to the tile in which it arose. Tiling artifacts are removed by averaging over every shift of the grid and over the symmetries of the square, and that average is weighted by the Poisson residual each pass leaves behind, so a pass whose tile boundaries fell on a discontinuity does not impose its seam on the result.

Experiments on synthetic and real data, against four reference algorithms from four distinct families and under six complementary metrics, show that the proposed method matches or improves on the state of the art. One of those metrics, a corrected cyclic re-wrap residual introduced in the paper, needs no ground truth and therefore remains available on real acquisitions.