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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。
The least squares method is one of the most robust methods for solving the problem of two-dimensional phase unwrapping. The essence of this method is to minimize the overall dispersion of the partial derivatives of the phase and the partial phase of the unwrapped phase in the least-square sense, Solve a large system of sparse linear equations. Due to the sparseness of the system matrix structure, convergence speed is very slow when using iterative method. In order to improve the convergence characteristics, a discrete wavelet transform phase unwrapping algorithm based on multi-resolution representation is proposed. Transform the original linear system into an equivalent new system with better convergence condition by using wavelet transform. Simulation results show that the proposed method can recover the true phase well, and its unwinding effect is better than Gauss-Seidel relaxation iteration and multi-grid method.