【正文】 ed 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 can be expressed as a sparse linear equation. anterior method is usually used to solve this large linear equation. However, a large putation time is required and therefore improving the convergence rate is a very important task when using this method. Some numerical algorithms have been applied to this problem to improve convergence conditions. An approach for fast convergence of a sparse linear equation is to transfer the original equation system into a new system with larger supports .Multiresolution or hierarchical representation concepts have often been used for this purpose. Recently, wavelet transform has been investigated deeply in science and engineering fields as a sophisticated tool for the multiresolution analysis of signals and systems. It deposes a signal space into its lowresolution subspace and the plementary detail subspaces. In our method, the discrete wavelet transform is applied to the linear system of least squares phase unwrapping problem to represent the original system in separate multiresolution spaces .In this new transferred system, a better convergence condition can be achieved. This method was briefly introduced in out previous work ,where the proposed method was applied only to the unweighted problem, In this paper, this new method is extended to the weighted least squares problem. Also, a full description of the proposed method is given here. 2 Weighted least squares phase unwrapping: a review Least squares phase obtains an unwrapped solution by minimizing the 2L norm between the discrete partial derivatives of the wrapped phase data and those of the unwrapped solution function. Given the wrapped phase ,ij? on an MN rectangular grid( 01iM? ? ? , 01jN? ? ? ),the partial derivatives of the wrapped phase are defined as ? ?, 1 , ,xi j i j i jW ???? ? ?, ? ?, , 1 ,yi j i j i jW ???? ? ? (1) Where W is the wrapping operator that wraps the phase into the interval ? ?,??? .The differences between the partial derivatives of the solution ,ij? and those in (1) can be minimized in the weighted least squares sense, by differentiating the sum ? ? ? ?22, 1 , , , , , 1 , ,x x y yi j i j i j i j i j i j i j i ji j i jww? ? ? ???? ? ? ? ? ? ??? (2) With respect to ,ij? and setting the result to zero. In (2),the gradient weights , ,xijw and ,yijw ,are used to prevent some phase values corrupted by noise or aliasing from degrading the unwrapping , and are defined by ? ?22, 1 , ,m in ,x i j i j i jw w w?? , ? ?22, , 1 ,m in ,y i j i j i jw w w?? , ,01ijw?? (3) The weighted least squares phase unwrapping problem is to find the solution ,ij? that minimizes the su