Do, Minh N.Vetterli, Martin2005-04-182005-04-182005-04-18200310.1109/TIP.2002.806252https://infoscience.epfl.ch/handle/20.500.14299/212767WOS:0001815652000023206The ridgelet transform (Candès and Donoho, 1999) was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines. In this paper, we propose an or- thonormal version of the ridgelet transform for discrete and fi- nite-size images. Our construction uses the finite Radon transform (FRAT) (Bolker, 1987:Matùs and Flusser, 1993) as a building block. To overcome the periodiza- tion 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.waveletsrigeletsRadon transformdirectional basesdiscrete transformsnon-linear approximationimage representationimage denoisingtext::journal::journal article::research article