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Curvelets and Ridgelets

  • Reference work entry
Computational Complexity

Article Outline

Glossary

Definition of the Subject

Introduction

Ridgelets

Curvelets

Stylized Applications

Future Directions

Bibliography

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Abbreviations

WT1D:

The one‐dimensional Wavelet Transform as defined in [53]. See also Numerical Issues When Using Wavelets.

WT2D:

The two‐dimensional Wavelet Transform.

Discrete ridgelet trasnform (DRT):

The discrete implementation of the continuous Ridgelet transform.

Fast slant stack (FSS):

An algebraically exact Radon transform of data on a Cartesian grid.

First generation discrete curvelet transform (DCTG1):

The discrete curvelet transform constructed based on the discrete ridgelet transform.

Second generationdiscrete curvelet transformx (DCTG2):

The discrete curvelet transform constructed based on appropriate bandpass filtering in the Fourier domain.

Anisotropic elements:

By anistropic, we mean basis elements with elongated effective support; i. e. \( \mathrm{length} > \mathrm{width} \).

Parabolic scaling law:

A basis element obeys the parabolic scaling law if its effective support is such that \( \text{width} \approx \text{length}^2 \).

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Author information

Authors and Affiliations

  1. GREYC CNRS UMR 6072, ENSICAEN, Caen Cedex, France

    Jalal Fadili

  2. Laboratoire Astrophysique des Interactions Multi‐échelles UMR 7158, CEA/DSM‐CNRS‐Universite Paris Diderot, SEDI-SAP, Gif‐sur‐Yvette Cedex, France

    Jean-Luc Starck

Authors
  1. Jalal Fadili
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Fadili, J., Starck, JL. (2012). Curvelets and Ridgelets. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_48

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