Robustness of phase retrieval methods in x‐ray phase contrast imaging: A comparison

Abstract

Purpose: 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. Methods: 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. Results: 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. Conclusions: 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.

X-ray phase-shifts-based method of volumetric breast density measurement

“…(5) and called this as the phase-attenuation duality (PAD). 21 We found that when the phase-attenuation duality holds, the x-ray propagation equation gets simplified and the phase map can be retrieved from just a single phase-sensitive projection I ( r D ) of the imaged object: 21,22 …”

“…21 Recently, we have theoretically and experimentally demonstrated that the PAD-based phase retrievals are robust against the noise, in a stark contrast to the TIE-based method that is unstable in the presence of noise in images. 22 Of course, in order for breast tissues to fulfill the phase-attenuation duality condition, the tube voltages should be set to as high as 120-150 kVp, grossly different from the tube voltages employed in current mammography, where tube voltages used are lower than 40 kVp. Although the attenuation-based tissue contrast gets much reduced at 120-150 kVp, the phase-contrast extracted from the phase retrieval will compensate for the attenuationcontrast loss associated with the use of high tube voltages.…”

X-Ray Phase Imaging for Breast Cancer Detection

“…This stark comparison shows that the conventional TIE-based phase retrieval method is unstable against the noise in the wrap's projection images, while the AP-based phase retrieval method is shown in the experiment to be superior to the TIE-based method for the robustness in performing the phase retrieval. For details, please refer to [Yan, Wu, Liu 2011].…”

“…This result advanced the understanding of the image contrast mechanism of phase contrast tomography. For details, please refer to [Yan and Wu 2011]. …”

“…This stark comparison shows that the conventional TIE-based phase retrieval method is unstable against the noise in the wrap's projection images, while the AP-based phase retrieval method is shown in the experiment to be superior to the TIE-based method for the robustness in performing the phase retrieval. For details, please refer to [Yan, Wu, Liu 2011].Extending the research works on the phase retrieval methods, as a by-product of this project, we made a progress in understanding the apparent linear attenuation coefficients in the inline phase contrast tomography. In the inline phase contrast x-ray tomography the reconstructed apparent linear attenuation coefficient values in the tomography may be greatly larger than sample's linear attenuation coefficients or even be negative.…”