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

By E.J. Candes. 2002

273 citations recorded by the source corpus.

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Citations in the corpus

Solving Inverse Problems With Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity (2010, methodology): “Relative to pre-fixed dictionaries s uch as wavelets [53], curvelets [11], and bandlets [54], learne d dictionaries enjoy the advantage of being better adapted to the images, thereby enhancing the sparsity.”
Sparse Coding via Thresholding and Local Competition in Neural Circuits (2008, background): “Natural images can be well-approximated by a small subset of elements from an overcomplete dictionary (Field, 1994; Olshausen, 2003; Candès and Donoho, 2004).”
Transforms and Operators for Directional Bioimage Analysis: A Survey. (2016, background): “Over the past decade, curvelets (Candès and Donoho 2004), shearlets (Labate et al.”
Full length article: Compactly supported shearlets are optimally sparse (2011, unknown): “This initiated the introduction of a different model, called cartoon-like model (see [5, 19, 1]), which revealed the suboptimal treatment of edges by wavelets.”
Wavelets with composite dilations and their MRA properties (2006, background): “As shown in [4,7], this property is needed to obtain representations that are optimally sparse for functions in a certain class.”
Directionlets: anisotropic multidirectional representation with separable filtering (2006, background): “bandelets [11], [12]) or non-adaptive (edgelets and wedgelets [13]–[17], curvelets [18]–[20], contourlets [21], etc.”
Nonhomogeneous Wavelet Systems in High Dimensions (2010, background): “However, as pointed out in [3], for high dimensional problems, directionality of a transform is an important feature.”
A Shearlet Approach to Edge Analysis and Detection (2009, unknown): “The shearlet transform has similarities to the curvelet transform, first introduced by Candès and Donoho [10], [22].”
WIRE: Wavelet Implicit Neural Representations (2023, background): “…highly anisotropic spatial localization is well-suited for certain kinds of data, many natural data (e.g., photographic images) are best represented using a combination of atoms with isotropic and anisotropic spatial localization (e.g., wavelets and curvelets [9] or wavelets and wedgelets [50]).”
Super-Resolution With Sparse Mixing Estimators (2010, background): “Curvelet frames [10] and contourlet frames [20 ] build sparse image approximations by taking advantage of the image directional regularity.”