Two-dimensional phase unwrapping based on the finite element method and FFT's

In the paper, the least squares solutions of the two-dimensional phase unwrapping problem are obtained by the finite element method and the fast Fourier transform. It extends the wrapped phase function to a periodic even function using a well-known mirror reflection([11]), and the resulting equation derived by the finite element method([16]) is solved using the fast Fourier transform. A noise-robust extension of the proposed technique is efficiently implemented by the finite element method and the fast Fourier transform. Since the differences between the least-squares unwrapped phase and the wrapped phase should be equal to the integer number of 2 pi([16]), we will determine an integer number of 2 pi on each pixel and make the wrapped phase plus the integer number of 2 pi closest to the least-squares unwrapped phase.