Fast Discrete Curvelet Transforms

By E.J. Candes, Laurent Demanet, David L. Donoho, Lexing Ying. Multiscale Modeling & simulation, 2006

2,764 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/376d81bd72028b827a2e538967907cac9fbf2890

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

The Curvelet Transform (2010, neutral): “Finally, we summarize the properties of the obtained curve-let elements.”
Compressive sensing for seismic data reconstruction via fast projection onto convex sets based on seislet transform (2016, methodology): “The well-known exited sparsity-promoting transforms in the exploration geophysics field include the Fourier(Bochner and Chandrasekharan, 1949), wavelet transform(Akansu et al., 2010), and curvelet transform (Candès et al., 2006a).”
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging (2011, positive): “Figure 10 (d) shows the result but now using to be the fast discrete curvelet transform [5].”
Wave atoms and sparsity of oscillatory patterns (2007, methodology): “An example of quantitative success story is curvelets, which were designed for the purpose of providing a sparse expansion of curved edges [8,9,31], bandlimited wavefronts [7] and other geometric features in images.”
Closed-loop surface-related multiple elimination and its application to simultaneous data reconstruction (2015, methodology): “Other parameterizations using the curvelet transform (Candes et al., 2006; Herrmann et al., 2007, 2008; Herrmann and Verschuur, 2008) or the wavelet transform (Liu et al., 1995) are also possible candidates for a sparse representation of the seismic data.”
Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal (2008, neutral): “Second, new multiscale transforms have been recently proposed such as the fast curvelet transform [51] and the wave atom transform [52], and it would also be very interesting to investigate how our MS-VST could be linked to”
Non-parametric seismic data recovery with curvelet frames (2008, methodology): “(15) There are numerous papers that study the behavior of this optimization problem (see e.g. Candès et al., 2006b).”
The curvelet representation of wave propagators is optimally sparse (2004, methodology): “authors along with Donoho and Ying recently proposed two architectures for a Digital Curvelet Transform, one via Unequispaced Fast Fourier Transforms, and one using a Wedge Wrapping technique [ 5 ].”
Retinal Image Analysis Using Curvelet Transform and Multistructure Elements Morphology by Reconstruction (2011, methodology): “and is optimal in the sense that no other representation can yield a smaller asymptotic error with the same number of terms [9].”
The SURE-LET Approach to Image Denoising (2007, background): “[51], Curvelets [52, 53], Directionlets [54], Contourlets [55]) or complex basis functions (e.”
Morphological Component Analysis: An Adaptive Thresholding Strategy (2007, background): “Morphological Component Analysis : An Adaptive Thresholding Strategy Jérôme Bobin, Jean-Luc Starck, Jalal M. Fadili, Yassir Moudden, David L. Donoho To cite this version: Jérôme Bobin, Jean-Luc Starck, Jalal M. Fadili, Yassir Moudden, David L. Donoho.”
Comparisons of wavelets, contourlets and curvelets in seismic denoising (2009, positive): “Consider the poor performance of the classical FFT on a nonstandard Cartesian grid, one can use an unequispaced fast FFT (USFFT) or a wrapping technique as addressed in Candès et al. (2006).”
Dreamlet-based interpolation using POCS method (2014, methodology): “Curvelet transform (Candes et al., 2006), which works better for curved seismic events compared with Fourier-based methods, is also used in seismic interpolation (Herrmann and Hennenfent, 2008).”
An introduction to continuous optimization for imaging (2016, background): “An important discovery in recent years (Candès et al. 2006b, Donoho 2006, Aharon et al. 2006) is the observation that many real-world signals can be modelled via sparse representation in a suitable basis or ‘dictionary’.”
Fast Image Recovery Using Variable Splitting and Constrained Optimization (2009, neutral): “The goal of our splitting is not to address the difﬁculty raised by a non-separable and non-quadratic regularizer, but to exploit second order (Hessian) information of the function f 1 , as will be shown below.”