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Interior Tomography from Differential Phase Contrast Data via Hilbert Transform Based on Spline Functions.

Qingsong Yang1, Wenxiang Cong1, Ge Wang1

  • 1Biomedical Imaging Center, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.

Proceedings of Spie--The International Society for Optical Engineering
|June 6, 2017
PubMed
Summary

This study introduces a novel iterative method using spline functions to reconstruct interior regions from X-ray differential phase contrast (DPC) imaging data. The technique overcomes challenges with data truncation and noisy measurements for improved soft tissue imaging.

Keywords:
Differential Phase Contrast ImagingHilbert TransformInterior Tomography

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Area of Science:

  • Medical Imaging
  • Biophysics
  • Computational Imaging

Background:

  • X-ray phase contrast imaging offers high sensitivity for soft biological tissues.
  • Grating-based differential phase contrast (DPC) imaging utilizes standard X-ray tubes but faces grating fabrication challenges.
  • Data truncation from size-limited gratings creates an interior problem in DPC imaging.

Purpose of the Study:

  • To develop a robust method for reconstructing interior regions of interest (ROIs) from truncated DPC data.
  • To address the instability and inaccuracy of differential operations in traditional DPC interior reconstruction.
  • To enable high-resolution imaging of large biological samples using DPC.

Main Methods:

  • An iterative reconstruction algorithm based on spline functions was proposed.
  • Differential DPC data were back-projected into image space.
  • A system matrix incorporating Hilbert transforms of spline bases was computed for iterative solving.
  • Compressed sensing principles and prior information were integrated into the iterative process.

Main Results:

  • The proposed iterative method successfully reconstructed interior ROIs from DPC data.
  • The algorithm demonstrated stability and accuracy even with noisy differential data.
  • The method effectively handled data truncation issues inherent in large object imaging.

Conclusions:

  • The spline-based iterative method provides a viable solution for the DPC interior problem.
  • This approach enhances the applicability of grating-based DPC imaging for large-scale biological studies.
  • The developed algorithm paves the way for advanced phase imaging of soft tissues.