A comparative study of two fast phase unwrapping algorithms. (Q1421258)

Let \(I= \{1,2,\dots, N\}\times \{1,2,\dots, N\}\). The two-dimensional phase unwrapping problem consists in the reconstruction of a function \(u: I\to\mathbb{R}\) from the knowledge of the function values modulus \(2\pi\). Two methods are studied: the discrete Fourier method proposed by \textit{M. Costantini}, \textit{A. Farina} and \textit{F. Zirilli} [A fast phase unwrapping algorithm for SAR interferometry, IEEE Transactions on Geoscience and Remote Sensing 37, 452--460 (1999)] and the network optimization method (NOM) due to \textit{M. Costantini}, \textit{A. Farina} and \textit{F. Zirilli} [A novel phase unwrapping method based on network programming, IEEE Transations on Geoscience and Remote Sensing 36, 813--821 (1998)]. It is shown that the methods do not compute the same solution, so a revised version of the first method is introduced which is equivalent to the second method. The results are based on a singular value decomposition (SVD) of the matrix defining the linear constraints of the optimization problem arising in the NOM. It is mentioned that the SVD produces various results involving lattice graphs.