基于小波变换的最小二乘相位解缠算法

Least squares phase unwrapping algorithm based on the wavelet transform

最小二乘法是求解二维相位解缠问题最稳健的方法之一,其本质是在最小二乘意义下使缠绕相位的离散偏导数与解缠相位的偏导数整体偏差最小,并等效为可求解一大型的稀疏线性方程系统。由于系统矩阵结构的稀疏性,在采用迭代法求解时收敛速度非常慢。为了改善收敛特性,提出一种基于多分辨率表示的离散小波变换相位解缠算法。利用小波变换将原线性系统转化成具有较好收敛条件的等价新系统。仿真实验表明,该方法能够很好的恢复真实相位,其解缠效果优于Gauss-Seidel松弛迭代和多重网格法。

Least squares phase unwrapping algorithm is one of the robust methods to solve the two-dimensional phase unwrapping problem. This method obtains a least-squares solution by minimizing the differences between the discrete partial derivatives of the wrapped phase function and those of the unwrapped solution function. The least squares solution is equivalent to the solution of a large sparse linear equation. Owing to its sparse structure, the convergence rate of the iterative method is very slow. To improve this condition, the wavelet transform method based on multiresolution representation is proposed. By applying the wavelet transform, the original system is converted into an equivalent linear system with better convergence condition. This speeds up the overall system convergence rate. The simulation experiment shows that the proposed algorithm provides better result than those obtained by the Gauss-Seidel relaxation and the multigrid method.