The finite ridgelet transform for image representation.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 18237876.
- Also identified by DOI 10.1109/TIP.2002.806252.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
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.