Curvelets are a non- adaptive technique for multi-scale object representation. Being an extension of the wavelet concept, they are becoming popular in similar fields, namely in image processing and scientific computing. Wavelets generalize the Fourier transform by using a basis that represents both location and spatial frequency.

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.

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:

Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needle-shaped elements at fine scales. This pyramid is nonstandard, however. Indeed, curvelets have useful geometric features that set …

Discrete Curvelet Transform Curvelets then and now Curvelets were introduced in 1999 by Candès and Donoho to address the edge representation problem. The definition they gave was based on windowed ridgelets. In 2002, they simplified the definition of curvelets and constructed a new tight frame. In 2003, they developed a Continuous Curvelet ...

The Curvelet Frame Applications of Curvelets Application to wave flow Images with jumps along curves Candés-Donoho (2003) Approximation rate is optimal: Choose n largest coefficients c in f = P c ’ kf fnk2 L2. n 2 log(n)3 No frame can do better for jumps along C2 curves. Wavelet expansion: kf fnk2 L2. n 1 Hart F. Smith An Introduction to ...

CurveLab is a toolbox implementing the Fast Discrete Curvelet Transform, both in Matlab and C++. The latest version is 2.1.2. The paper Fast Discrete Curvelet Transforms explains the curvelet transforms in detail.

In this paper, we present a review on the curvelet transform, including its history beginning from wavelets, its logical relationship to other multiresolu-tion multidirectional methods like contourlets and shearlets, its basic theory and discrete algorithm.

the curvelet transform refines the scale-space view-point by adding an extra element, orientation, and operates by measuring information about an object at specified scales and locations but only along specified orientations. The specialist will rec-ognize the connection with ideas from microlocal analysis. The joint localization in both space and

Curvelets are two dimensional waveforms that provide a new architecture for multiscale analysis. In space, a curvelet at scale j is an oriented “needle” whose effective support is a 2−j by 2−j/2 rectangle and thus obeys the parabolic scaling relation width ≈ length2.