Sparse multidimensional representation using shearlets

By Demetrio Labate, Wang-Q Lim, Gitta Kutyniok, Guido L. Weiss. SPIE Optics + Photonics, 2005

555 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Media Technology

View Paper: https://www.semanticscholar.org/paper/501eb48fa061aacd014643215d6ecf04993c9cf5

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In Computer Vision and Pattern Recognition

In Media Technology

Citations in the corpus

The Curvelet Transform (2010, background): “Steerable wavelets [28], [59], Gabor wavelets [40], wedgelets [23], beamlets [24], bandlets [51], [54], contourlets [21], shearlets [39], [31], wave atoms [20], platelets [67], and surfacelets [42] have been proposed independently to identify and restore geometric features.”
Fast Discrete Curvelet Transforms (2006, background): “The idea of using concentric squares and shears is also central to the construction of tight frames of “shearlets” by Guo, Kutyniok, Labate, Lim, Weiss, and Wilson in a recent series of papers [28, 29, 30] starting with [28].”
The Cosparse Analysis Model and Algorithms (2011, unknown): “In signal and image processing, discrete transforms such as wavelet, Gabor, curvelet, contourlet, shearlet, and others [33, 39, 13, 27], are of interest, and this empirical observation seems to give a good support for the sparse synthesis model.”
Wave atoms and sparsity of oscillatory patterns (2007, unknown): “Various alternative transforms have since then been proposed for representing edges in images, often with their own performance analysis as well: contourlets [17], bandelets [28], shearlets [24].”
Modern regularization methods for inverse problems (2018, background): “ natural images in wavelet bases (cf. [274, 225, 273, 341]). Further improvements were made by replacing the orthonormal bases by frames (cf. [126]) such as curvelets (cf. [97, 98]) or shearlets (cf. [257, 197, 256]). Sparsity is naturally measured by the ‘0-norm, the number of nonzero entries. Sinc”
Sparse directional image representations using the discrete shearlet transform (2008, methodology): “In addition, the shearlet approach can be associated to a multiresolution analysis [22,27].”
Dictionaries for Sparse Representation Modeling (2010, unknown): “The shearlet transform [67]–[69] is a recently proposed alternative to curvelets, which utilizes structured shear operations rather than rotations to control orientation.”
Adaptive wavelet methods for solving operator equations: An overview (2009, methodology): “Besides aggregated wavelet frames, here we only mention curvelets ([CD04]) and shearlets ([ LLKW05 ]).”
Optimally Sparse Multidimensional Representation Using Shearlets (2007, background): “This is particularly useful for the development of fast algorithmic implementations of these transformations [23, 25].”
Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation (2010, methodology): “For natural images, dictionaries such as Wavelets [22], Curvelets [23], Contourlets [24], and Shearlets [25], all provide fast transforms.”
Resolution of the wavefront set using continuous shearlets (2006, methodology): “We refer to [13, 15, 16, 17, 18, 22 , 21] for more detail about the research about shearlets.”
Transforms and Operators for Directional Bioimage Analysis: A Survey. (2016, background): “Over the past decade, curvelets (Candès and Donoho 2004), shearlets (Labate et al. 2005; Yi et al. 2009; Kutyniok and Labate 2012), and contourlets (Do and Vetterli 2005) have attracted a lot of interest.”
Full length article: Compactly supported shearlets are optimally sparse (2011, unknown): “[17] D.”