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.

Some recent articles related to the curvelet transform as implemented in CurveLab.


L. Demanet, L. Ying, Curvelets and Wave Atoms for Mirror-Extended Images, 2007. A new variant of the FDCT that extends the ideas of "wavelets on an interval" to curvelets and wave atoms.

E. J. Candes, L. Demanet, D. L. Donoho, L. Ying, Fast Discrete Curvelet Transforms, 2005. This is our reference for the definition of curvelets in the discrete setting.

L. Ying, L. Demanet, E. J. Candes, 3D Discrete Curvelet Transform, 2005.

E. J. Candes, L. Demanet, The Curvelet Representation of Wave Propagators is Optimally Sparse, 2004.

E. J. Candes, D. L. Donoho, Continuous Curvelet Transform II: Discretization and Frames, 2003.

E. J. Candes, D. L. Donoho, Continuous Curvelet Transform I: Resolution of the Wavefront Set, 2003.

E. J. Candes, D. L. Donoho, New Tight Frames of Curvelets and Optimal Representations of Objects with Smooth Singularities, 2002. This is our reference for the definition of curvelets in the continuous setting.

E. J. Candes, L. Demanet, Curvelets and Fourier Integral Operators, 2002.

E. J. Candes, F. Guo, New Multiscale Transforms, Minimum Total Variation Synthesis: Applications to Edge-Preserving Image Reconstruction, 2002.