A general local reconstruction approach based on a truncated Hilbert transform

  • Authors:

  • Yangbo Ye;Hengyong Yu;Yuchuan Wei;Ge Wang

  • Affiliations:

  • Department of Mathematics, University of Iowa, Iowa City, IA;CT Laboratory, Biomedical Imaging Division, VT-WFU School of Biomedical Engineering, Virginia Tech., Blacksburg, VA;CT Laboratory, Biomedical Imaging Division, VT-WFU School of Biomedical Engineering, Wake Forest University, Winston-Salem, NC;CT Laboratory, Biomedical Imaging Division, VT-WFU School of Biomedical Engineering, Virginia Tech, Blacksburg, VA and CT Laboratory, Biomedical Imaging Division, VT-WFU School of Biomedical Engin ...

  • Venue:
  • Journal of Biomedical Imaging
  • Year:
  • 2007

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Abstract

Exact image reconstruction from limited projection data has been a central topic in the computed tomography (CT) field. In this paper, we present a general region-of-interest/volume-of-interest (ROI/VOI) reconstruction approach using a truly truncated Hilbert transform on a line-segment inside a compactly supported object aided by partial knowledge on one or both neighboring intervals of that segment. Our approach and associated new data sufficient condition allows the most flexible ROI/VOI image reconstruction from the minimum account of data in both the fan-beam and cone-beam geometry. We also report primary numerical simulation results to demonstrate the correctness and merits of our finding. Our work has major theoretical potentials and innovative practical applications.