Investigation On Theory And Algorithm Of Phase Unwrapping Based On Least-Squares

Synthetic Aperture Radar interferometry (InSAR) developed at the end of the1960’s, which took the phase information extracted from the complex data image for its data source, gotting the3D information of the earth surface and information to elevation changes.Compared with optical remote measure, because it is protected from light and weather effects, and it can work all day and all time, still can obtain the characteristics of the subject under the surface or ground vegetation coverage, caused a lot of attention all over the world.The basic principle is:through the antenna pair on the sensor or two satellite in the same orbit to image the same ground or water surface, get two of complex data image, after registration、coherent computation and phase unwrapping get phase difference image and then invert the surface deformation and elevation information. After interference process, the phase image is the result from wrapping the real phase image, it must through the phase unwrapping to recover its real phase. Phase unwrapping is the most important step in InSAR. It directly affect the accuracy of the surface deformation measurement and digital elevation model accuracy. So far, phase unwrapping algorithm has kinds. They generally fall into two categories:path-following methodology and the minimum-norm methods. A common path-following methodology for phase unwrapping is to begin at a grid point and integrate the wrapped phase differences over the branch cuts after detecting residues that prevent the unwrapping path from crossing the lines. The minimum-norm methods formulate the phase unwrapping problem in a generalized minimum-norm sense. The most widely applied in the minimum-norm methods is the least-square method,that achieve the sum of the squared differences between the gradients of the solution and those of the measurements is minimized.This article mainly introduces the thoery and algorithm of the least-square phase-unwrapping method.And then based on the analysis of the commonly used data in InSAR and use the programming language of c#, combined with the echnology of WPS and GIS, successfully achieved the InSAR phase unwrapping software for least-square algorithm.Finally.the article analyses the precision of the least-square algorithm achieved by the InSAR phase unwrapping software.and use this tools to analyse the manner of the least-square algorithm applied to phase unwrapping.and compare the difference between Goldstein branch-cut algorithm and the least square algorithm,and the influence of the iteraion in the least square algorithm.