Unwrapping Phase Images: Theory and Applications Using Probabilistic Inference Techniques

Koetter 摘要二维拓扑中的相位展开是一个信号处理问题，在过去 20 年中得到了广泛的研究，并具有重要的应用，例如医学成像和合成孔径雷达。 然而，尽管二维网格中的相位展开在科学和工程中很重要，但迄今为止，它仍然是一个本质上未解决的问题。 这项研究采用概率推理的方法来解决这个问题。 这项工作不仅有望产生基于和积算法和结构化变分方法的强大相位展开方案，而且有可能为相位展开问题的不适定性质和可解性提供深入的理论见解。 这种见解对于指导实用算法的开发极其重要。这项研究的主要目标是开发和完善用于相位展开的算法，这些算法是通用的、高效的，并且显着改进了早期的方法。在这种情况下的指导思想之一是使用概率推断作为相位展开方案中的非线性预处理步骤。 初步实验已经证实，通过这种方法确实可以显着提高传统技术的性能。 这项研究的成功可以产生深远的实际影响。 例如，在SAR干涉测量中，相位展开是生成地形高程图的重要步骤，这项工作可以显着提高基于确定性相位模型的现有算法的精度。 同样，拟议的工作将使使用磁共振成像（MRI）信号的常规相位成像变得可行，这将显着扩展 MRI 的临床效用。

Koetter AbstractPhase unwrapping in 2-dimensional topologies is a signal-processing problem that has been extensively studied over the past 20 years and has important applications, such as medical imaging and synthetic aperture radar. However, despite its importance in science and engineering, to date, phase unwrapping in 2-dimensional grids has remained an essentially unsolved problem. This research takes a fresh approach to the problem using methods from probabilistic inference. The work not only holds the promise of resulting in powerful phase unwrapping schemes based on the sum-product algorithm and structured variational methods, but also has the potential to provide deep theoretical insight into the ill-posed nature and solvability of the phase unwrapping problem. Such an insight is extremely important for guiding the development of practical algorithms.The main objective of this research is to develop and refine algorithms for phase unwrapping that are versatile, efficient and that significantly improve upon earlier approaches. One of the guiding ideas in this context is the use of probability inference as a nonlinear preprocessing step in a phase unwrapping scheme. Initial experiments have confirmed that the performance of traditional techniques can indeed be significantly boosted with such an approach. Success of this research can have a profound practical impact. For example, in SAR interferometry, phase unwrapping is an essential step in generating terrain elevation maps, and this work can significantly enhance the accuracy of existing algorithms based on deterministic phase models. Similarly, the proposed work will make routine phase imaging using Magnetic Resonance Imaging (MRI) signals feasible, which will significantly extend the clinical utility of MRI.