The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Ridgelets: a key to higher-dimensional intermittency?
Abstract
In dimensions two and higher, wavelets can efficiently represent only a small range of the full diversity of interesting behaviour. In effect, wavelets are well adapted for point–like phenomena, whereas in dimensions greater than one, interesting phenomena can be organized along lines, hyperplanes and other non–point–like structures, for which wavelets are poorly adapted.We discuss in this paper a new subject, ridgelet analysis, which can effectively deal with line–like phenomena in dimension 2, plane–like phenomena in dimension 3 and so on. It encompasses a collection of tools which all begin from the idea of analysis by ridge functions ψ(u1x1 + ⃛ + unxn whose ridge profiles ψ are wavelets, or alternatively from performing a wavelet analysis in the Radon domain.The paper reviews recent work on the continuous ridgelet transform (CRT), ridgelet frames, ridgelet orthonormal bases, ridgelets and edges and describes a new notion of smoothness naturally attached to this new representation.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · Mathematics of Control, Signals, and Systems · doi:10.1007/bf02551274 · Cited by 13,883
Cited by
Fast Discrete Curvelet Transforms
Candès, E., Demanet, L., Donoho, D., & Ying, L. (2006) · Multiscale Modeling & Simulation · doi:10.1137/05064182x · Cited by 2,573
Self-citationNew tight frames of curvelets and optimal representations of objects with piecewise C2 singularities
Candès, E. J., & Donoho, D. L. (2004) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.10116 · Cited by 1,545
Self-citationWedgelets: nearly minimax estimation of edges
Donoho, D. L. (1999) · The Annals of Statistics · doi:10.1214/aos/1018031261 · Cited by 638
Self-citationSparse multidimensional representation using shearlets
Labate, D., Lim, W.-Q., Kutyniok, G., & Weiss, G. (2005) · SPIE Proceedings · doi:10.1117/12.613494 · Cited by 455
Research Progress of Visual Inspection Technology of Steel Products—A Review
Sun, X., Gu, J., Tang, S., & Li, J. (2018) · Applied Sciences · doi:10.3390/app8112195 · Cited by 109
Metadata
- Authors
- Candès, E. J., & Donoho, D. L.
- Venue
- Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- Publisher
- The Royal Society
- Published
- 1999-09
- Volume
- 357
- Issue
- 1760
- Pages
- 2495-2509
- ISSN
- 1364-503X (ISSN-L)
- 1471-2962
- OpenAlex
- W2066462711
- Cited by
- 893
- References
- 1
- FWCI
- 20.54
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Ridgelets: a key to higher-dimensional intermittency? https://app.cochat.ai/papers/10.1098/rsta.1999.0444
- The paper
- Candès, E. J., & Donoho, D. L. (1999). Ridgelets: a key to higher-dimensional intermittency? Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences. https://doi.org/10.1098/rsta.1999.0444
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
