Filtered backprojection reconstruction algorithm for tomography

Samit Basu, Yoram Bresler

Research output: Contribution to journalArticlepeer-review

Abstract

We present a new fast reconstruction algorithm for parallel beam tomography. The new algorithm is an accelerated version of the standard filtered backprojection (FBP) reconstruction, and uses a hierarchical decomposition of the backprojection operation to reduce the computational cost from O( 3) to O( 2log 2 ). We discuss the choice of the various parameters that affect the behavior of the algorithm, and present numerical studies that demonstrate the cost versus distortion tradeoff. Comparisons with Fourier reconstruction algorithms and a recent multilevel inversion algorithm by Brandt et al., both of which also have O( 2log 2 ) cost, suggest that the proposed hierarchical scheme has a superior cost versus distortion performance. It offers rms reconstruction errors comparable to the FBP with considerable speedup. For an example with a 512 × 512-pixel image and 1024 views, the speedup achieved with a particular implementation is over 40 fold, with reconstructions visually indistinguishable from the FBP.

Original languageEnglish (US)
Pages (from-to)1760-1773
Number of pages14
JournalIEEE Transactions on Image Processing
Volume9
Issue number10
DOIs
StatePublished - 2000

Keywords

  • Fast algorithm
  • Fast reconstruction
  • Filtered backprojection
  • Hierarchical
  • Tomography

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition

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