The finite ridgelet transform for image representation

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 (FRA...

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Veröffentlicht in:IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - 12(2003), 1 vom: 28., Seite 16-28
1. Verfasser: Do, Minh N (VerfasserIn)
Weitere Verfasser: Vetterli, Martin
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2003
Zugriff auf das übergeordnete Werk:IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
Schlagworte:Journal Article
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520 |a 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 
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