Comments on the filtered backprojection algorithm, range conditions, and the pseudoinverse solution

Mark A. Anastasio, Xiaochuan Pan, Eric W Clarkson

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

The filtered backprojection (FBP) algorithm is widely used in computed tomography for inverting the two-dimensional Radon transform. In this paper, we analyze the processing of an inconsistent data function by the FBP algorithm (in its continuous form). Specifically, we demonstrate that an image reconstructed using the FBP algorithm can be represented as the sum of a pseudoinverse solution and a residual image generated from an inconsistent component of the measured data. This reveals that, when the original data function is in the range of the Radon transform, the image reconstructed using the FBP algorithm corresponds to the pseudoinverse solution. When the data function is inconsistent, we demonstrate that the FBP algorithm makes use of a nonorthogonal projection of the data function to the range of the Radon transform.

Original languageEnglish (US)
Pages (from-to)539-542
Number of pages4
JournalIEEE Transactions on Medical Imaging
Volume20
Issue number6
DOIs
StatePublished - Jun 2001

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Radon
Tomography
Processing

Keywords

  • Computed tomography
  • Filtered backprojection algorithm
  • Radon transform

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

Cite this

Comments on the filtered backprojection algorithm, range conditions, and the pseudoinverse solution. / Anastasio, Mark A.; Pan, Xiaochuan; Clarkson, Eric W.

In: IEEE Transactions on Medical Imaging, Vol. 20, No. 6, 06.2001, p. 539-542.

Research output: Contribution to journalArticle

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