含噪声包裹相位图的加权最小二乘相位展开算法研究

二维相位展开广泛应用在精密光学测量、自适应光学、合成孔径雷达、图像处理等领域中。为处理含噪声包裹相位图,以预条件共轭斜量法求解权重最小二乘相位展开方程。引入非加权二维离散余弦变换求解泊松方程得到的最小二乘相位解作为共轭斜量法的初始解,从而加快了收敛速度,同时提出一种新质量图确定算法求解过程中的权重项。计算机模拟和试验表明算法计算速度快,能有效地消除传统路径积分法在处理信噪比低包裹相位图时的"拉线"现象,是一种有效的相位展开方法。

Weighted least-square phase unwrapping algorithm for noisy phase-map

Two-dimensional phase unwrapping is widely applied in a variety of fields including optical interferometry,adaptive optics,synthetic-aperture radar and image processing.Although path-following phase unwrapping method is successful in some application,the algorithm has its own drawbacks in processing wrapped-phase images with bugs.In order to process the wrapped phase with noise,preconditioner conjugate gradient method(PCG) is applied to solve the weighted least-squares phase unwrapping problem.The preconditioner is obtained by solving an unweighted least-square phase unwrapping problem.The discrete Poisson equation is solved by means of discrete cosine transform(DCT).This algorithm converges much faster than the Picard algorithm.The maximum phase gradient is adopted to determine the weights.Computer simulation and experimental examples make it clear that the preconditioner conjugate method works successfully when noise exist in wrapped phase images.