A comparative study of two fast phase unwrapping algorithms

Let u be a real function defined on a rectangular grid. The (two-dimensional) phase unwrapping problem consists in the reconstruction of u from the knowledge of its values modulus 2pi. We study two different methods for the solution of this problem: the Fourier transform method and the network optimization method. We show that these methods do not compute the same solution, so that we introduce a revised version of the Fourier transform method which is equivalent to the network optimization method. These results are based on an explicit expression for a singular value decomposition of A, where A is the matrix that defines the linear constraints of the optimization problem arising in the network optimization method. (C) 2003 Elsevier Inc. All rights reserved.