Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges

By E.J. Candes, David L. Donoho. 2000

1,811 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0843c2f5cbd7dda30cbeed73d95b77d068408476

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Citations in the corpus

Sketch-based shape retrieval (2012, methodology): “The Curvelet basis is the maximally sparse representation for such data [Candès and Donoho 1999] and, consequently, we design our descriptor based on ideas taken from this transformation.”
A Tutorial on Speckle Reduction in Synthetic Aperture Radar Images (2013, background): “Recently, multiresolution transforms embedding directional information, such as contourlets [41], curvelets [42], [43], and many others, have been successfully applied to denoising in general and despeckling in particular.”
Directional multiresolution image representations (2002, methodology): “The original curvelet construction of Candès and Donoho [20] uses block ridgelet transforms implies a mixture of rectangular and polar grids, and thus it is difficult to see how the embedded grids of approximation can be defined.”
Sparsity- and continuity-promoting seismic image recovery with curvelet frames (2008, background): “Fourier (and also wavelet) transforms are known to perform poorly on this type of functions [9,12].”
Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach (2010, background): “It was introduced to approximate, in a nonadaptive manner, curved singularities—e.g., wavefronts—with very few curvelet coefficients (Candès and Donoho, 2000, 2004).”
Directional multiscale modeling of images using the contourlet transform (2006, background): “Some examples include the steerable pyrami d [13], brushlets [14], complex wavelets [15], and the curvel et transform [16].”
Near-ideal model selection by ℓ1 minimization (2008, background): “• sinusoids are best for oscillatory phenomena; • wavelets [18] are best for point-like singularities; • curvelets [7, 8] are best for curve-like singularities (edges); • local cosines are best for textures; and so on.”
Non-linear primary-multiple separation with directional curvelet frames (2007, methodology): “D functions with singularities on piece-wise C2 curves, the non-linear approximation rates are sub optimal for both Fourier and separable wavelets (Candès & Donoho 2000a,b),∥∥ f − f FK ∥∥22 ∝ K − 12 (A8) and∥∥ f − f WK ∥∥22 ∝ K −1, (A9) compared to the rate obtained by adaptive triangulation∥∥ f −…”
Retinal Image Analysis Using Curvelet Transform and Multistructure Elements Morphology by Reconstruction (2011, background): “In the past decade, Candès and Donoho [8] introduced the curvelet transform, a new multiscale transform.”
Non-parametric seismic data recovery with curvelet frames (2008, methodology): “This incapability explains why wavelets do not improve the compression rate for data with wavefronts as much as recently developed directional curvelet frames do (Candès and Donoho, 2000a, 2004; Candès and Donoho, 2005a,b).”