title: Robustness of phase retrieval methods in X-ray phase contrast imaging: a comparison.
abstract: OBJECTIVE
  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.
authors: Department of Radiology, University of Alabama, Birmingham, AL 35233, USA.
authors: Aimin
authors: A
authors: Yan
authors: Xizeng
authors: X
authors: Wu
authors: Hong
authors: H
authors: Liu
mesh_terms: D007091:Image Processing, Computer-Assisted / Q000379:methods*; D019047:Phantoms, Imaging; D011829:Radiation Dosage; D014057:Tomography, X-Ray Computed / Q000379:methods*