Department of Radiology, University of Alabama, Birmingham, AL 35233, USA.
Med Phys. 2011 Sep;38(9):5073-80. doi: 10.1118/1.3618731.
The robustness of the phase retrieval methods is of critical importance for limiting and reducing radiation doses involved in x-ray phase contrast imaging. This work is to compare the robustness of two phase retrieval methods by analyzing the phase maps retrieved from the experimental images of a phantom.
Two phase retrieval methods were compared. One method is based on the transport of intensity equation (TIE) for phase contrast projections, and the TIE-based method is the most commonly used method for phase retrieval in the literature. The other is the recently developed attenuation-partition based (AP-based) phase retrieval method. The authors applied these two methods to experimental projection images of an air-bubble wrap phantom for retrieving the phase map of the bubble wrap. The retrieved phase maps obtained by using the two methods are compared.
In the wrap's phase map retrieved by using the TIE-based method, no bubble is recognizable, hence, this method failed completely for phase retrieval from these bubble wrap images. Even with the help of the Tikhonov regularization, the bubbles are still hardly visible and buried in the cluttered background in the retrieved phase map. The retrieved phase values with this method are grossly erroneous. In contrast, in the wrap's phase map retrieved by using the AP-based method, the bubbles are clearly recovered. The retrieved phase values with the AP-based method are reasonably close to the estimate based on the thickness-based measurement. The authors traced these stark performance differences of the two methods to their different techniques employed to deal with the singularity problem involved in the phase retrievals.
This comparison shows that the conventional TIE-based phase retrieval method, regardless if Tikhonov regularization is used or not, is unstable against the noise in the wrap's projection images, while the AP-based phase retrieval method is shown in these experiments to be superior to the TIE-based method for the robustness in performing the phase retrieval.
在 X 射线相衬成像中，限制和降低所涉及的辐射剂量，相位恢复方法的稳健性至关重要。本工作通过分析体模实验图像的相位图来比较两种相位恢复方法的稳健性。
比较了两种相位恢复方法。一种方法基于强度传输方程（TIE）用于相衬投影，基于 TIE 的方法是文献中最常用的相位恢复方法。另一种是最近开发的基于衰减-分区（AP）的相位恢复方法。作者将这两种方法应用于空气泡包装体模的实验投影图像中，以恢复泡包装的相位图。比较了使用这两种方法获得的相位图。
在使用基于 TIE 的方法获得的包装相位图中，无法识别气泡，因此，该方法完全无法从这些泡包装图像中进行相位恢复。即使使用 Tikhonov 正则化，气泡仍然难以看到，并且在检索的相位图中被杂乱的背景所掩盖。该方法的检索相位值存在严重误差。相比之下，在使用 AP 基方法获得的包装相位图中，气泡被清晰地恢复。AP 基方法的检索相位值与基于厚度测量的估计值相当接近。作者将这两种方法的显著性能差异归因于它们在处理相位恢复中涉及的奇点问题时所采用的不同技术。
本比较表明，传统的基于 TIE 的相位恢复方法，无论是否使用 Tikhonov 正则化，在包装的投影图像中的噪声下都是不稳定的，而在这些实验中，AP 基方法在执行相位恢复的稳健性方面优于基于 TIE 的方法。
