CT reconstruction from parallel and fan-beam projections by a 2-D discrete radon transform

Amir Averbuch; Ilya Sedelnikov; Yoel Shkolnisky

doi:10.1109/TIP.2011.2164416

CT reconstruction from parallel and fan-beam projections by a 2-D discrete radon transform

Amir Averbuch^*, Ilya Sedelnikov, Yoel Shkolnisky

^*Corresponding author for this work

Samsung Israel Research Center

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

The discrete Radon transform (DRT) was defined by Abervuch as an analog of the continuous Radon transform for discrete data. Both the DRT and its inverse are computable in O(n ²log n) operations for images of size n × n. In this paper, we demonstrate the applicability of the inverse DRT for the reconstruction of a 2-D object from its continuous projections. The DRT and its inverse are shown to model accurately the continuum as the number of samples increases. Numerical results for the reconstruction from parallel projections are presented. We also show that the inverse DRT can be used for reconstruction from fan-beam projections with equispaced detectors.

Original language	English
Article number	5981387
Pages (from-to)	733-741
Number of pages	9
Journal	IEEE Transactions on Image Processing
Volume	21
Issue number	2
DOIs	https://doi.org/10.1109/TIP.2011.2164416
State	Published - Feb 2012

Keywords

2-D discrete Radon transform (DRT)
Computed tomography (CT)
fan-beam projections
parallel projections
tomography

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10.1109/TIP.2011.2164416

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title = "CT reconstruction from parallel and fan-beam projections by a 2-D discrete radon transform",

abstract = "The discrete Radon transform (DRT) was defined by Abervuch as an analog of the continuous Radon transform for discrete data. Both the DRT and its inverse are computable in O(n 2log n) operations for images of size n × n. In this paper, we demonstrate the applicability of the inverse DRT for the reconstruction of a 2-D object from its continuous projections. The DRT and its inverse are shown to model accurately the continuum as the number of samples increases. Numerical results for the reconstruction from parallel projections are presented. We also show that the inverse DRT can be used for reconstruction from fan-beam projections with equispaced detectors.",

keywords = "2-D discrete Radon transform (DRT), Computed tomography (CT), fan-beam projections, parallel projections, tomography",

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AB - The discrete Radon transform (DRT) was defined by Abervuch as an analog of the continuous Radon transform for discrete data. Both the DRT and its inverse are computable in O(n 2log n) operations for images of size n × n. In this paper, we demonstrate the applicability of the inverse DRT for the reconstruction of a 2-D object from its continuous projections. The DRT and its inverse are shown to model accurately the continuum as the number of samples increases. Numerical results for the reconstruction from parallel projections are presented. We also show that the inverse DRT can be used for reconstruction from fan-beam projections with equispaced detectors.

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CT reconstruction from parallel and fan-beam projections by a 2-D discrete radon transform

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