What is Curvelets Homepage (curvelet.org)?

curvelet.org is the official homepage for the curvelet transform and the CurveLab toolbox. It is the place to go if you want to understand what curvelets are, read the underlying papers, or download the CurveLab software for image processing, inverse problems, and scientific computing. The site is maintained by Emmanuel Candes, Laurent Demanet, David Donoho, and Lexing Ying.

What the site covers

The homepage introduces the curvelet transform as a higher-dimensional generalization of the wavelet transform, designed to represent images at different scales and different angles. It highlights two mathematical properties that motivate the transform:

• Curved singularities can be well approximated with very few coefficients, and in a non-adaptive manner — hence the name "curvelets."
• Curvelets remain coherent waveforms under the action of the wave equation in a smooth medium.

Beyond the conceptual overview, the site points to the papers where the theory is developed and to the CurveLab toolbox, which the team released to encourage the dissemination of curvelets to image processing, inverse problems, and scientific computing.

Software: CurveLab

The newest version listed on the site is CurveLab 2.1.2 (April 2008), which includes mirror-extended (ME) curvelets. If you are looking for the reference implementation of the curvelet transform, this is the release the homepage points to.

Related resource

The site also notes a sister webpage for the wave atom transform at Waveatom.org, useful if your interest extends to related multiscale transforms.

Who it is for

curvelet.org is aimed at researchers and practitioners working on:

• Image processing
• Inverse problems
• Scientific computing

If you need the theory, start with the papers linked from the homepage. If you need to run the transform, go to the CurveLab download.