New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities

By E.J. Candes, David L. Donoho. 2004

1,717 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Computer Vision and Pattern Recognition

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Citations in the corpus

Wavelets on Graphs via Spectral Graph Theory (2009, neutral): “A large family of alternative multiscale transforms has been developed and used extensively for image processing, including Laplacian pyramids [22], steerable wavelets [23], complex dual-tree wavelets [24], curvelets [25], and bandlets [26].”
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? (2004, background): “For instance, certain classes of oscillatory signals have rapidly decaying Gabor coefficients [10], certain types of images with discontinuities along edges have rapidly decaying curvelet coefficients [11] and so on.”
Sparse Coding via Thresholding and Local Competition in Neural Circuits (2008, methodology): “LETTER Communicated by Michael Lewicki Sparse Coding via Thresholding and Local Competition in Neural Circuits Christopher J. Rozell∗ crozell@gatech.edu Don H. Johnson dhj@rice.edu Richard G. Baraniuk richb@rice.edu Department of Electrical and Computer Engineering, Rice University, Houston, TX…”
Continuous curvelet transform: II. Discretization and frames (2005, methodology): “3 Interpretation The frame that we have just constructed is almost identical to the discrete curvelets frame proposed by Candès and coauthors [1, 2, 3]; that frame is set up so that the frame elements are real valued; it can be be produced from this one by averaging together terms at θj, with those ”
The Application of Compressed Sensing for Photo-Acoustic Tomography (2009, background): “While a wavelet is defined by a scale and a position, a curvelet is defined by a scale, a position and an angle, leading to an almost optimal representation of images containing edges [18].”
Blind motion deblurring from a single image using sparse approximation (2009, methodology): “We use the curvelet system (Candes and Donoho [8]) to find the sparse approximation to the blur kernel under curvelet domain.”
NONPARAMETRIC ESTIMATION OF COMPOSITE FUNCTIONS (2009, background): “Note that the approach of [4, 5] is conceptually different, and does not rely on pointwise selection rules.”
Near-ideal model selection by ℓ1 minimization (2008, background): “For instance: • 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.”
Transforms and Operators for Directional Bioimage Analysis: A Survey. (2016, background): “Over the past decade, curvelets (Candès and Donoho, 2004), shearlets (Kutyniok and Labate, 2012; Labate et al, 2005; Yi et al, 2009), and contourlets (Do and Vetterli, 2005) have attracted a lot of interest.”
Fusion frames and g-frames (2008, neutral): “Nice properties of frames make them very useful in characterization of function spaces and other fields of applications such as filter bank theory [3], sigma–delta quantization [2], signal and image processing [4] and wireless communications [11].”
Practical Signal Recovery from Random Projections (2005, background): “Perhaps the most notable of these, the wavelet transform [10], [11] and its later geometric extensions [12], have found widespread use due to their suitability for general classes of piecewise smooth signals, especially photograph-like images (see Figure 2).”
Optimally Sparse Multidimensional Representation Using Shearlets (2007, methodology): “Following the approach in [7], we suppose that, for j > j 0 , the scale 2 − j is small enough so that over the square − 2 − j ≤ x 1 , x 2 ≤ 2 − j the edge curve may be parametrized as (cid:181) (cid:182) (cid:181) (cid:182) (the case where j ≤ j 0 is small requires a much simpler analysis and will…”
The Nonsubsampled Contourlet Transform: Theory, Design, and Applications (2006, background): “In particular, it can satisfy the a nisotropic scaling law — a key property in establishing the expansion nonlinear approxim ation behavior [12], [13].”
Compressed sensing (2006, methodology): “Again in the image processing setting, we use the - model discussed in Candès and Donoho [39], [40].”