Unwrapping Phase Images: Theory and Applications Using Probabilistic Inference Techniques

Koetter摘要二维拓扑中的相位展开是近20年来被广泛研究的一个信号处理问题，在医学成像和合成孔径雷达等领域有着重要的应用。然而，尽管它在科学和工程中的重要性，到目前为止，二维网格中的相位展开仍然是一个基本上没有解决的问题。本研究运用概率推理的方法对这一问题进行了全新的研究。这项工作不仅有望产生基于和积算法和结构变分方法的强大的位相展开方案，而且有可能对位相展开问题的病态性质和可解性提供深入的理论见解。该研究的主要目的是开发和完善通用的、高效的相位展开算法，并在已有算法的基础上有显著的改进。本文的指导思想之一是使用概率推理作为相位展开方案中的非线性预处理步骤。初步实验证实，这种方法确实可以显著提高传统技术的性能。这项研究的成功可以产生深远的实践影响。例如，在合成孔径雷达干涉测量中，相位展开是生成地形高程图的关键步骤，这项工作可以显著提高现有基于确定性相位模型的算法的精度。同样，这项拟议的工作将使使用磁共振成像(MRI)信号的常规相位成像成为可能，这将显著扩展MRI的临床应用。

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.