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Proceedings Paper

Some links between continuous and discrete Radon transform
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Paper Abstract

The Filtered BackProjection is still questionable since many discrete versions have been derived from the continuous Radon formalism. From a continuous point of view, a previous work has made a link between continuous and discrete FBP versions denoted as Spline 0-FBP model leading to a regularization of the infinite Ramp filter by the Fourier transform of a trapezoidal shape. However, projections have to be oversampled (compared to the pixel size) to retrieve the theoretical properties of Sobolev and Spline spaces. Here we obtain a novel version of the Spline 0 FBP algorithm with a complete continuous/discrete correspondence using a specific discrete Radon transform, the Mojette transform. From a discrete point of view, the links toward the FBP algorithm are shaped with the morphological description and the extended use of discrete projection angles. The resulting equivalent FBP scheme uses a selected set of angles which covers all the possible discrete Katz's directions issued from the pixels of the (square) shape under reconstruction: this is implemented using the corresponding Farey's series. We present a new version of a discrete FBP method using a finite number of projections derived from discrete geometry considerations. This paper makes links between these two approaches.

Paper Details

Date Published: 12 May 2004
PDF: 11 pages
Proc. SPIE 5370, Medical Imaging 2004: Image Processing, (12 May 2004); doi: 10.1117/12.533472
Show Author Affiliations
Myriam C. J. Servieres, IRCCyN-CNRS (France)
Ecole Polytechnique de l'Univ. de Nantes (France)
Nicolas Normand, IRCCyN-CNRS (France)
Ecole Polytechnique de l'Univ. de Nantes (France)
Peggy Subirats, IRCCyN-CNRS (France)
Ecole Polytechnique de l'Univ. de Nantes (France)
JeanPierre Guedon, IRCCyN-CNRS (France)
Ecole Polytechnique de l'Univ. de Nantes (France)

Published in SPIE Proceedings Vol. 5370:
Medical Imaging 2004: Image Processing
J. Michael Fitzpatrick; Milan Sonka, Editor(s)

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