Two dimensional phase unwrapping of interferometric SAR data by means of wavelet technique

Abstract

One of the reliable methods in least-squares method is multigrid technique which overcomes the problem of slow convergence and less-accurate of Gauss-Seidel by transforming problem to coarser grid. It makes a pyramid of grids. Each grid has half the resolution of its predecessor. It uses two restriction and prolongation operators called fine-to-coarse and coarse-to-fine operators respectively. In this research, discrete wavelet decomposition and its reconstruction have been applied on the two operators. One of the assumptions made on this operator is that as long as the wavelet transformation decomposes the 2-D signal to one low frequency and three high frequency components, it should converge faster and more accurate than the multigrid method. This is due to the fact that the transformation of only low frequency component would suffice rather than transforming the whole grid to coarser grid. The idea has been implemented and tested on simulation data and the results confirm the assumption. In this paper the results of implementation of various wavelet filters and also multigrid techniques on various simulation data (with and without noise) are presented. In all cases, wavelet techniques have shown improved results than multigrid techniques.