CT gradient image reconstruction directly from projections

Shaojie Tang, Xuanqin Mou, Junfeng Wu, Hao Yan, Hengyong Yu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


An algorithm is proposed to directly reconstruct a CT gradient image in a region of interest(ROI). First, the central slice theorem is generalized and a differential constraint condition (DCC) is introduced in parallel-beam geometry. Then, an algorithm is developed to reconstruct the gradient images in both Cartesian and polar coordinate systems based on a two-step Hilbert transform method. Finally, the reconstruction algorithm is extended into the equi-distant fan-beam geometry. Meanwhile, a conditional truncation for projection data acquisition is permitted by using a one-dimensional(1-D) finite Hilbert transform in image domain. Because the reconstructed gradient image is in terms of local operator, it have a better performance in CT image analysis and other CT applications compared to the global Calderon operator in Lambda Tomography.

Original languageEnglish (US)
Pages (from-to)173-198
Number of pages26
JournalJournal of X-Ray Science and Technology
Issue number2
StatePublished - Jun 22 2011


  • Computed tomography
  • hilbert transform
  • lambda tomography
  • region of interest

ASJC Scopus subject areas

  • Radiation
  • Instrumentation
  • Radiology Nuclear Medicine and imaging
  • Condensed Matter Physics
  • Electrical and Electronic Engineering


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