Shear-based fast hierarchical backprojection for parallel-beam tomography

Ashvin K. George, Yoram Bresler

Research output: Contribution to journalArticlepeer-review


We introduce a family of fast algorithms for 2-D parallel-beam tomographic backprojection. They aggregate the projections in a hierarchical structure involving the shearing and addition of sparsely sampled images. The algorithms achieve a computational cost of O(N2 log P), when backprojecting an N × N pixel image from P projections. The algorithms provide a systematic means, guided by a Fourier-domain interpretation, to adjust and optimize the tradeoff between computational cost and accuracy. In an example with N = 512 and P = 1458 the algorithms provide high accuracy, with more than an order of magnitude reduction in operation counts.

Original languageEnglish (US)
Pages (from-to)317-334
Number of pages18
JournalIEEE transactions on medical imaging
Issue number3
StatePublished - Mar 2007


  • Backprojection
  • Fast algorithm
  • Image shear
  • Radon transform
  • Spline interpolation
  • Tomography

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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