2012
DOI: 10.1109/tip.2011.2164416
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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(2) log 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 par… Show more

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Cited by 35 publications
(14 citation statements)
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“…Many recent researchers have shown the interest of Radon transform such as image processing [10] and pattern recognition [11,12]. Using this method, the image is mapped with lines into a subspace of intensities.…”
Section: Proposed Methodsmentioning
confidence: 99%
“…Many recent researchers have shown the interest of Radon transform such as image processing [10] and pattern recognition [11,12]. Using this method, the image is mapped with lines into a subspace of intensities.…”
Section: Proposed Methodsmentioning
confidence: 99%
“…A fast and accurate PPFT calculation method was proposed by the same group in [10,14] and has been used in different tomography based modalities such as electron microscopy [19,20,21], X-ray absorption and phase-contrast CT [22]. In [22,19], TV smoothing is used iteratively with forward/backward application of PPFT to reduce the artifacts which are made by incompleteness of the available data.…”
Section: Relation With Prior Workmentioning
confidence: 99%
“…In [22,19], TV smoothing is used iteratively with forward/backward application of PPFT to reduce the artifacts which are made by incompleteness of the available data. In [14], a 2D Discrete radon transform is proposed for fanbeam geometry for linear X-ray movement. Here we used a new combination of CST, CS and PPFT to improve our CS-based CT reconstructions.…”
Section: Relation With Prior Workmentioning
confidence: 99%
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“…Unfortunately, the Shepp-Logan phantom is still largely used in papers that focus on 2D image reconstruction [19, 20, 21, 22, 23, 24, 25, 26, 27, 28]. We attribute this situation to the fact that software for data simulation with the Shepp-Logan phantom is not readily applicable to the FORBILD head phantom.…”
Section: Introductionmentioning
confidence: 99%