Computing with Curvelets: From Image Processing to Turbulent Flows

The curvelet transform allows an almost optimal nonadaptive sparse representation for curve-like features and edges. The authors describe some recent applications involving image processing, seismic data exploration, turbulent flows, and compressed sensing.

[1]  E. Candès,et al.  Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges , 2000 .

[2]  Jianwei Ma,et al.  Three-dimensional curvelets for coherent vortex analysis of turbulence , 2007 .

[3]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[4]  Demetrio Labate,et al.  Optimally Sparse Multidimensional Representation Using Shearlets , 2007, SIAM J. Math. Anal..

[5]  Emmanuel J. Candès,et al.  The curvelet transform for image denoising , 2002, IEEE Trans. Image Process..

[6]  François-Xavier Le Dimet,et al.  Curvelet-Based Snake for Multiscale Detection and Tracking of Geophysical Fluids , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[7]  Emmanuel J. Candès,et al.  The curvelet transform for image denoising , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[8]  Stéphane Mallat,et al.  Sparse geometric image representations with bandelets , 2005, IEEE Transactions on Image Processing.

[9]  Laurent Demanet,et al.  Fast Discrete Curvelet Transforms , 2006, Multiscale Model. Simul..

[10]  Fionn Murtagh,et al.  Gray and color image contrast enhancement by the curvelet transform , 2003, IEEE Trans. Image Process..

[11]  R. Neelamani,et al.  Coherent and random noise attenuation using the curvelet transform , 2008 .

[12]  Lexing Ying,et al.  3D discrete curvelet transform , 2005, SPIE Optics + Photonics.

[13]  Ivan Bermejo-Moreno,et al.  On the non-local geometry of turbulence , 2008, Journal of Fluid Mechanics.

[14]  D. Donoho.  Wedgelets: nearly minimax estimation of edges , 1999 .

[15]  S. Dekel,et al.  Curvelets: a low-level framework for computer vision , 2007 .

[16]  Minh N. Do,et al.  Ieee Transactions on Image Processing the Contourlet Transform: an Efficient Directional Multiresolution Image Representation , 2022 .

[17]  Gerlind Plonka-Hoch,et al.  Combined Curvelet Shrinkage and Nonlinear Anisotropic Diffusion , 2007, IEEE Transactions on Image Processing.

[18]  E. Candès,et al.  New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities , 2004 .

[19]  F. Herrmann,et al.  Sparsity- and continuity-promoting seismic image recovery with curvelet frames , 2008 .

[20]  Felix J. Herrmann,et al.  Seismic denoising with nonuniformly sampled curvelets , 2006, Computing in Science & Engineering.

[21]  Gerlind Plonka-Hoch,et al.  Nonlinear Regularized Reaction-Diffusion Filters for Denoising of Images With Textures , 2008, IEEE Transactions on Image Processing.

[22]  Robert D. Nowak,et al.  Platelets: a multiscale approach for recovering edges and surfaces in photon-limited medical imaging , 2003, IEEE Transactions on Medical Imaging.

[23]  E. Candès,et al.  Ridgelets: a key to higher-dimensional intermittency? , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[24]  Huub Douma,et al.  Leading-order seismic imaging using curvelets , 2007 .

[25]  Jianwei Ma,et al.  Curvelets for surface characterization , 2007 .

[26]  N. Kingsbury.  Image processing with complex wavelets , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[27]  Myeong-Ryong Nam,et al.  Fusion of multispectral and panchromatic Satellite images using the curvelet transform , 2005, IEEE Geoscience and Remote Sensing Letters.

[28]  D. J. Verschuur,et al.  Adaptive curvelet-domain primary-multiple separation , 2008 .

[29]  Hervé Chauris,et al.  Seismic demigration/migration in the curvelet domain , 2008 .

[30]  Jianwei Ma,et al.  Combined Complex Ridgelet Shrinkage and Total Variation Minimization , 2006, SIAM J. Sci. Comput..

[31]  François-Xavier Le Dimet,et al.  Deblurring From Highly Incomplete Measurements for Remote Sensing , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[32]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[33]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.