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The Curvelet transform is a higher dimensional generalization of the Wavelet transform designed to represent images at different scales and different angles.  Curvelets enjoy two unique mathematical properties, namely:

• 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.  

More information can be found in the papers below.  By releasing the CurveLab toolbox, we hope to encourage the dissemination of curvelets to image processing, inverse problems and scientific computing.

The Curvelet.org team: Emmanuel Candes, Laurent Demanet, David Donoho, Lexing Ying.



Links

Some links on curvelets:


• Curvelets were introduced in 1999 by Candes and Donoho to address the edge representation problem, see Curvelets 99. The definition they gave was based on windowed ridgelets -- it is a bit different from the one we now use in CurveLab. An early implementation is presented here. Further applications include inverse problems with edges and curvilinear integrals.

Curvelet image denoising and image enhancement experiments based on the curvelet implementation described in this paper.

Morphological Component Analysis: Component Separation based on the curvelet transform, and applications for texture separation and inpainting.

• Curvelets in Astrophysics: Jean-Luc Starck.

• Curvelets in Seismic Imaging at UBC: Felix Herrmann and his crew (Peyman, Gilles). See this paper for spectacular denoising and compression experiments using the curvelet transform on non-equispaced synthetic seismic data.

• Curvelets in Seismic Imaging: Martijn de Hoop at Purdue, and Huub Douma at the Colorado School of Mines. Recent work in collaboration with Hart Smith, Gunter Uhlmann and Eric Dussaud.

• Curvelets in Seismic Imaging: Mauricio Sacchi and his PhD student Mostafa Naghizadeh recently (2009) proposed seismic data interpolation using curvelets, in this paper.

• Curvelets in Pure Math: Hart Smith was the first to construct a tight frame of curvelets, in the context of wave equations with low-regularity coefficients.

• Curvelets in Plasma Physics: Bedros Afeyan at Polymath.

• Contourlets: a curvelet-like transform based on filterbanks, by Minh Do and Martin Vetterli.

• Shearlets and wavelets with composite dilations: a curvelet-like approach within the framework of affine systems, by Demetrio Labate, Gitta Kutyniok and co-workers.

Waveatom.org: a webage on wave atoms, from the authors of CurveLab.

• The reference for wavelets is Wavelet.org. For the newest books on wavelets, check out: Books on Wavelets




Apologies to anybody who would feel left out of this list - please drop me an email at laurent at curvelet.org.



Last modified 24 August 2007 - Maintained by Laurent Demanet - -