Unwrapping phases by relaxed mean field inference

Some types of medical and topographic imaging device produce images in which the pixel values are “phase-wrapped”, i.e., measured modulus a known scalar. Phase unwrapping can be viewed as the problem of inferring the number of shifts between each and every pair of neighboring pixels, subject to an a priori preference for smooth surfaces, and subject to a zero curl constraint, which requires that the shifts must sum to 0 around every loop. We formulate phase unwrapping as a mean field inference problem in a probability model, where the prior favors the zero curl constraint. We compare our mean field technique with the least squares method on a synthetic 100 100 image, and give results on a larger 512 512 image.