3-D discrete analytical ridgelet transform
In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D t...
| Veröffentlicht in: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1997. - 15(2006), 12 vom: 20. Dez., Seite 3701-14 |
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| Weitere Verfasser: | , |
| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2006
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society |
| Schlagworte: | Journal Article Research Support, Non-U.S. Gov't |
| Zusammenfassung: | In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient |
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| Beschreibung: | Date Completed 04.01.2007 Date Revised 26.10.2019 published: Print Citation Status MEDLINE |
| ISSN: | 1057-7149 |