O(N 3 log N) backprojection algorithm for the 3-D radon transform

Samit Basu, Yoram Bresler

Research output: Contribution to journalArticlepeer-review


We present a novel backprojection algorithm for three-dimensional (3-D) radon transform data that requires O(N 3 log 2 N) operations for reconstruction of an N × N × N volume from O(N 2) plane-integral projections. Our algorithm uses a hierarchical decomposition of the 3-D radon transform to recursively decompose the backprojection operation. Simulations are presented demonstrating reconstruction quality comparable to the standard filtered backprojection, which requires O(N 5) computations under the same circumstances.

Original languageEnglish (US)
Pages (from-to)76-88
Number of pages13
JournalIEEE transactions on medical imaging
Issue number2
StatePublished - Feb 2002


  • 3-D radon transform
  • Backprojection
  • Cone beam tomography
  • Fast algorithm
  • Hierarchical

ASJC Scopus subject areas

  • Biomedical Engineering
  • Radiology Nuclear Medicine and imaging
  • Radiological and Ultrasound Technology
  • Electrical and Electronic Engineering
  • Computer Science Applications
  • Computational Theory and Mathematics

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