title: The finite ridgelet transform for image representation.
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.
authors.affiliation: Audiovisual Communications Laboratory, Department of Communication Systems, Swiss Federal Institute of Technology, Lausanne, Switzerland. minhdo@uiuc.edu
authors.forename: Minh N
authors.initials: MN
authors.lastname: Do
authors.forename: Martin
authors.initials: M
authors.lastname: Vetterli