Some links between continuous and discrete Radon transform

Myriam C. J. Servieres; Nicolas Normand; Peggy Subirats; JeanPierre Guedon

doi:10.1117/12.533472

12 May 2004 Some links between continuous and discrete Radon transform

Myriam C. J. Servieres, Nicolas Normand, Peggy Subirats, JeanPierre Guedon

Proceedings Volume 5370, Medical Imaging 2004: Image Processing; (2004) https://doi.org/10.1117/12.533472
Event: Medical Imaging 2004, 2004, San Diego, California, United States

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.

Citation Download Citation

Myriam C. J. Servieres, Nicolas Normand, Peggy Subirats, and JeanPierre Guedon "Some links between continuous and discrete Radon transform", Proc. SPIE 5370, Medical Imaging 2004: Image Processing, (12 May 2004); https://doi.org/10.1117/12.533472

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