Phase unwrapping is important for synthetic aperture radar interferometry. All current methods of phase evaluation produce a distribution module 2/spl pi/, so that the reconstruction of the correct phase field from the wrapped phase field, by applying a suitable unwrapping process, is needed. The problem of recovering the absolute phase field is ill-posed and can be solved only by introducing additional constraints on the final solution. Assuming a Gaussian model for noise and that the gradient of the true phase is everywhere less than /spl pi/ in magnitude, a solution can be found which approximates the first order wrapped gradient of the phase data. An approximation of the unwrapped phase can be retrieved by adopting a weighted least square approach, in which the phase data are weighted to avoid unwrapping across regions of corrupted phase. The corrupted phase data are caused by such SAR phenomena as layover, radar shadow and temporal decorrelation. D.C. Ghiglia et al. (1994), introduced the first practical algorithm for this weighted least squares approach to phase unwrapping. Their algorithm employes an iterative method based on Fourier or cosine transforms and a preconditioned conjugate gradient (PCG) method to solve the weighted least square equation. The PCG converges rapidly with phase unwrapping problems that do not have large phase discontinuities, but on phase data with large discontinuities it results very slow and requires many iterations to converge. M.D. Pritt (1996) proposed a multigrid technique to speed up the whole process, essentially when the phase has noise and large discontinuities. His algorithm is a full multi-grid technique which allows a theoretical decreasing of computing time up to 25 times in respect to the PCG one. In this paper a new numerical solver is presented, which can be used to approach the weighted least square problem as well as other more refined stabilisers. Their algorithm can be applied to any positive-definite quadratic cost functional used to solve the PU problem.
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机译：相位展开对于合成孔径雷达干涉测量非常重要。所有当前的相位评估方法产生分配模块2 / SPL PI /，使得需要通过应用合适的展开过程来从包装的相位区域重建正确的相位场。恢复绝对相字段的问题是不良的，并且只能通过在最终解决方案上引入额外的约束来解决。假设高斯模型用于噪声，并且真正阶段的梯度无处不在/ SPL PI /幅度小于/幅度，则可以找到解决方案，其近似于相位数据的第一阶包装梯度。可以通过采用加权最小二乘方法来检索未包装相的近似，其中加权相位数据以避免突破阶段区域的展开。损坏的相位数据是由Prover，雷达阴影和时间去相关性的这样的SAR现象引起的。 D.C. Ghiglia等。 （1994），介绍了这种加权最小二乘法的第一种实用算法来相位展开。它们的算法采用基于傅立叶或余弦变换的迭代方法和预先处理的共轭梯度（PCG）方法来解决加权最小方形方程。 PCG通过相位展开问题迅速收敛，没有大相中不连续性，而是在具有大不连续的相位数据上，它会非常慢，需要许多迭代来汇聚。 M.D. Pritt（1996）提出了一种多重技术，以加速整个过程，基本上当相位具有噪声和大的不连续性。他的算法是一种完整的多电网技术，其允许在PCG一个上的计算时间的理论降低到达25倍。在本文中，提出了一种新的数值求解器，其可用于接近加权最小二乘问题以及其他更精细的稳定剂。它们的算法可以应用于用于解决PU问题的任何正定的二次成本函数。
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