Weighted least-square phase unwrapping algorithm for noisy phase-map

Two-dimensional phase unwrapping is widely applied in a variety of fields including optical interferometry, adaptive optics, synthetic-aperture radar and image processing. Although path-following phase unwrapping method is successful in some application, the algorithm has its own drawbacks in processing wrapped-phase images with bugs. In order to process the wrapped phase with noise, preconditioner conjugate gradient method (PCG) is applied to solve the weighted least-squares phase unwrapping problem. The preconditioner is obtained by solving an unweighted least-square phase unwrapping problem. The discrete Poisson equation is solved by means of discrete cosine transform (DCT). This algorithm converges much faster than the Picard algorithm. The maximum phase gradient is adopted to determine the weights. Computer simulation and experimental examples make it clear that the preconditioner conjugate method works successfully when noise exist in wrapped phase images.