【正文】 中文 3300 字 附錄 A：英文原文 Least squares phase unwrapping in wavelet domain Abstract: Least squares phase unwrapping is one of the robust techniques used to solve twodimensional phase unwrapping problems. However, owing to its sparse structure, the convergence rate is very slow, and some practical methods have been applied to improve this condition. In this paper, a new method for solving the least squares twodimensional phase unwrapping problem is presented. This technique is based on the multiresolution representation of a linear system using the discrete wavelet transform. By applying the wavelet transform, the original system is deposed into its coarse and fine resolution levels. Fast convergence in separate coarse resolution levels makes the overall system convergence very fast. 1 introduction Twodimensional phase unwrapping is an important processing step in some coherent imaging applications, such as synthetic aperture radar interferometry(InSAR) and magic resonance imaging(MRI).In these processes, threedimensional information of the measured objects can be extracted from the phase of the sensed signals ,However, the obseryed phase data are wrapped principal values, which are restricted in a 2? modulus ,and they must be unwrapped to their true absolute phase values .This is the task of the phase unwrapping, especially for twodimensional problems. The basic assumption of the general phase unwrapping methods is that the discrete derivatives of the unwrapped phase at all grid points are less than ? in absolute value .With this assumption satisfied ,the absolute phase can be reconstructed perfectly by integrating the partial derivatives of the wrapped phase data. In the general case, however, it is not possible to recover unambiguously the absolute phase from the measured wrapped phase which is usually corrupted by noise or aliasing effects such as shadow, layover, etc. In such cases, the basic assumption is violated and the simple integration procedure cannot be applied owing to the phase inconsistencies caused by the contaminations. After Goldsteinet al introduced the concept of ‘residues’ in the twodimensional phase unwrapping problem of InSAR, many phase unwrapping approaches to cope with this problem have been investigated. Pathfollowing (or integrationbased) methods and least squares methods are the most representative two basic classes in this field. There have also been some other approaches such as Green methods, Bayesian regularization methods ,image processingbased methods, and modelbased methods. Least squares phase unwrapping ,established by Ghiglia and Romero, is one of the most robust techniques to solve the twodimensional phase unwrapping problem. This method obtains an unwrapped solution by minimizing the differences between the partial derivatives of the wrapped phase data and the unwrapped solution .Least squares method is divided into unweighted and weighted least squares phase unwrapping. To isolate the phase inconsistencies, a weighted least squares method should be used, which depresses the contamination effects by using the weighting arrays. Green methods and Bayesian methods are also based on the least squares scheme .But these methods are different from those of ,in the concept of phase inconsistency treatment. Thus, this paper concerns only the least squares phase unwrapping problem of Ghiglia’s category. The least squares method is welldefined mathematically and equivalent to the solution of Poisson’s partial differential equation, which c