Antonopoulos Georgios C, Steltner Benjamin, Heisterkamp Alexander, Ripken Tammo, Meyer Heiko
Biomedical Optics Department, Laser Zentrum Hannover e.V., Hanover, Germany.
Institute of Quantum Optics, Gottfried Wilhelm Leibniz Universität Hannover, Hanover, Germany.
PLoS One. 2015 Nov 24;10(11):e0143186. doi: 10.1371/journal.pone.0143186. eCollection 2015.
A variety of physical and biomedical imaging techniques, such as digital holography, interferometric synthetic aperture radar (InSAR), or magnetic resonance imaging (MRI) enable measurement of the phase of a physical quantity additionally to its amplitude. However, the phase can commonly only be measured modulo 2π, as a so called wrapped phase map. Phase unwrapping is the process of obtaining the underlying physical phase map from the wrapped phase. Tile-based phase unwrapping algorithms operate by first tessellating the phase map, then unwrapping individual tiles, and finally merging them to a continuous phase map. They can be implemented computationally efficiently and are robust to noise. However, they are prone to failure in the presence of phase residues or erroneous unwraps of single tiles. We tried to overcome these shortcomings by creating novel tile unwrapping and merging algorithms as well as creating a framework that allows to combine them in modular fashion. To increase the robustness of the tile unwrapping step, we implemented a model-based algorithm that makes efficient use of linear algebra to unwrap individual tiles. Furthermore, we adapted an established pixel-based unwrapping algorithm to create a quality guided tile merger. These original algorithms as well as previously existing ones were implemented in a modular phase unwrapping C++ framework. By examining different combinations of unwrapping and merging algorithms we compared our method to existing approaches. We could show that the appropriate choice of unwrapping and merging algorithms can significantly improve the unwrapped result in the presence of phase residues and noise. Beyond that, our modular framework allows for efficient design and test of new tile-based phase unwrapping algorithms. The software developed in this study is freely available.
多种物理和生物医学成像技术，如数字全息术、干涉合成孔径雷达（InSAR）或磁共振成像（MRI），除了能够测量物理量的幅度外，还能测量其相位。然而，相位通常只能以模2π的方式测量，得到所谓的包裹相位图。相位解缠是从包裹相位中获取潜在物理相位图的过程。基于瓦片的相位解缠算法的操作方式是，首先对相位图进行镶嵌，然后对各个瓦片进行解缠，最后将它们合并成一个连续的相位图。它们可以高效地进行计算实现，并且对噪声具有鲁棒性。然而，在存在相位残差或单个瓦片解缠错误的情况下，它们容易失败。我们试图通过创建新颖的瓦片解缠和合并算法，以及创建一个允许以模块化方式组合它们的框架来克服这些缺点。为了提高瓦片解缠步骤的鲁棒性我们实现了一种基于模型的算法，该算法有效利用线性代数来解缠各个瓦片。此外，我们对一种已有的基于像素的解缠算法进行了改编，以创建一个质量引导的瓦片合并算法。这些原创算法以及先前存在的算法都在一个模块化的相位解缠C++框架中实现。通过检查解缠和合并算法的不同组合，我们将我们的方法与现有方法进行了比较。我们可以表明，在存在相位残差和噪声的情况下，解缠和合并算法的适当选择可以显著改善解缠结果。除此之外，我们的模块化框架允许对新的基于瓦片的相位解缠算法进行高效设计和测试。本研究中开发的软件可免费获取。
