The finite ridgelet transform for image representation.
- Do MN Audiovisual Communications Laboratory, Department of Communication Systems, Swiss Federal Institute of Technology, Lausanne, Switzerland. minhdo@uiuc.edu
- Vetterli M
- 2008-02-02
Published in:
- IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 2003
English
The ridgelet transform was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines. We propose an orthonormal version of the ridgelet transform for discrete and finite-size images. Our construction uses the finite Radon transform (FRAT) as a building block. To overcome the periodization effect of a finite transform, we introduce a novel ordering of the FRAT coefficients. We also analyze the FRAT as a frame operator and derive the exact frame bounds. The resulting finite ridgelet transform (FRIT) is invertible, nonredundant and computed via fast algorithms. Furthermore, this construction leads to a family of directional and orthonormal bases for images. Numerical results show that the FRIT is more effective than the wavelet transform in approximating and denoising images with straight edges.
- Language
-
- English
- Open access status
- green
- Identifiers
-
- DOI 10.1109/TIP.2002.806252
- PMID 18237876
- Persistent URL
- https://sonar.ch/global/documents/104912
Statistics
Document views: 39
File downloads:
- Full-text: 0