Where to Find Papers and More Information About Curvelets

The starting point is curvelet.org, the Curvelets Homepage maintained by the team behind the transform. The site states directly that "more information can be found in the papers," and it points to a sister resource for a related transform. If you want the primary literature rather than a summary, that homepage is the intended gateway.

What curvelet.org provides

The homepage is a compact reference page rather than a full documentation portal. Its stated contents:

• CurveLab 2.1.2 (April 2008) — described as the newest version, and the one that includes mirror-extended (ME) curvelets.
• A pointer to the papers — the site's own route to the underlying publications.
• A sister webpage for the wave atom transform at Waveatom.org.
• The team list: Emmanuel Candès, Laurent Demanet, David Donoho, and Lexing Ying.

The site frames the toolbox release as a way to "encourage the dissemination of curvelets to image processing, inverse problems, and scientific computing," so the papers and the toolbox are meant to be used together.

Why the papers matter for understanding curvelets

The homepage gives the two mathematical properties that distinguish curvelets from wavelets, and both are claims you would verify in the papers:

1. Sparse representation of curved singularities. Curved singularities can be well approximated with very few coefficients, and in a non-adaptive manner — which is where the name "curvelets" comes from.
2. Coherence under the wave equation. Curvelets remain coherent waveforms under the action of the wave equation in a smooth medium.

The transform itself is described as a higher-dimensional generalization of the wavelet transform, designed to represent images at different scales and different angles. That angular component is the key difference from wavelets, and it is the part worth reading the papers for.

How to use the site to find what you need

1. Open curvelet.org and locate the reference to the papers.
2. Follow that link to reach the publications by the listed team members.
3. If your interest is the discrete implementation rather than the theory, note that the same page hosts the CurveLab release — the toolbox and the papers are presented as a pair.
4. If your work involves wave atoms rather than curvelets, go to Waveatom.org, the sister site named on the homepage.

Expected result: you end up at the primary papers and, if needed, the CurveLab toolbox, rather than at a secondary summary.

Common sticking points

• The version is old. CurveLab 2.1.2 dates to April 2008. The homepage presents it as the newest version, so do not expect a more recent release to be listed there.
• The homepage is thin by design. It is a signpost, not a tutorial. Expect to do the actual reading in the papers.
• Curvelets are not wavelets. If you arrive expecting a wavelet-style multiresolution description alone, the angular and curved-singularity aspects are the parts that require the papers to understand properly.

Quick reference