The finite ridgelet transform for image representation
Top Cited Papers
- 20 March 2003
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Image Processing
- Vol. 12 (1) , 16-28
- https://doi.org/10.1109/tip.2002.806252
Abstract
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.Keywords
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