Quadratic regularization functionals for phase unwrapping
Quadratic regularization functionals for phase unwrapping
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DOI：
10.1364/josaa.12.002393
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发表时间：
1995-11
影响因子：
1.9
通讯作者：
J. Marroquín;M. Rivera
中科院分区：
文献类型：
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作者：
J. Marroquín;M. Rivera
在Hadamard意义下，去包裹一个有噪声的主值相场，或者等价地从有噪声的和可能不完全的相位差中重建一个去包裹的相场的问题可以被认为是不适定的。我们应用Thikonov正则化理论来寻找对应于正定二次代价泛函极小值的解。这些方法可以被认为是展开问题的经典最小二乘解的推广；正则化项的引入允许减少噪声(即使该噪声不会产生积分路径不一致)，并且以稳定和可控的方式在具有缺失数据的区域上内插解，并且以最小的计算复杂性增加。文中还讨论了用变换方法求直接解的算法和迭代过程的实现。在合成测试图像上的实验结果说明了这些方法的性能。
The problem of unwrapping a noisy principal-value phase field or, equivalently, reconstructing an unwrapped phase field from noisy and possibly incomplete phase differences may be considered ill-posed in the sense of Hadamard. We apply the Thikonov regularization theory to find solutions that correspond to minimizers of positive-definite quadratic cost functionals. These methods may be considered generalizations of the classical least-squares solution to the unwrapping problem; the introduction of the regularization term permits the reduction of noise (even if this noise does not generate integration-path inconsistencies) and the interpolation of the solution over regions with missing data in a stable and controlled way, with a minimum increase of computational complexity. Algorithms for finding direct solutions with transform methods and implementations of iterative procedures are discussed as well. Experimental results on synthetic test images are presented to illustrate the performance of these methods.