Two-Dimensional Wavelets and their Relatives: References

By Jean-Pierre Antoine, R. Murenzi, Pierre Vandergheynst, Syed Twareque Ali. 2004

341 citations recorded by the source corpus.

Subfields: Demography, Genetics, Political Science and International Relations

View Paper: https://www.semanticscholar.org/paper/dbcc550afcde577db6700c04c1f996593cbe516c

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In Genetics

1. Tomaso A. Poggio
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Citations in the corpus

• Unsupervised learning of invariant representations with low sample complexity: the magic of sensory cortex or a new framework for machine learning? (2013, background): “While (a) is well-known (b) is less so (but see p.41 in [43]).”
• Wavelet transform on manifolds: Old and new approaches (2010, neutral): “(a) The two-sphere S2 The construction of a CWT on the two-sphere S2 with help of the stereographic projection has been thoroughly treated in the literature [1, 3, 4], so we just quote the results.”
• Unsupervised Learning of Invariant Representations in Hierarchical Architectures (2013, background): “provided with the metric [2] (together with [3]) holds for nonlinearities with Lipschitz constants Lηn such that Nmaxn(Lηn) < 1.”
• A meteoroid stream survey using the Canadian Meteor Orbit Radar: I. Methodology and radiant catalogue (2008, positive): “…wavelet transform we use makes use of the Mexican Hat mother wavelet (which is well suited to point distributions having Gaussian shapes of enhancements; cf. Antoine, 2004): Wc(x0, y0) = 1√ 2πa +∞∫ −∞ +∞∫ −∞ f (x, y) ( 2 − (x0 − x) 2 + (y0 − y)2 a2 ) × exp [ − ( (x0 − x)2 + (y0 − y)2 2a2 )] dx dy.”
• A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction (2015, background): “…k (in fact, k is the index of the direction described by the rotation matrix r k ), and where λ = ( j, k ) ∈ Λ W \{ ( − J, 0) } are directional wavelets [30], [44], [45] with (complex-valued) mother wavelet and J ∈ Z corresponds to the coarsest scale resolved by the directional wavelets (2).”
• p-exponent and p-leaders, Part II: Multifractal Analysis. Relations to Detrended Fluctuation Analysis (2015, methodology): “r CMC-LN (left) and CMC-LP (right), single realizations of the random elds are plotted in Fig.5(top); we use the scaling range j1 = 3 and j2 = 8 and tensor-product Daubechies’ wavelet with N = 2 (cf. [74]). The observations and conclusions are similar to those obtained in the previous subsection for”
• A Shearlet Approach to Edge Analysis and Detection (2009, neutral): “For example, using wavelets, in order to identify corner points, one has to design a set of filters which is very different from the one used to detect the smooth edges [29].”
• Coorbit spaces and wavelet coefficient decay over general dilation groups (2012, background): “This is the similitude group in two dimensions, and it is the first systematically studied higher-dimensional dilation group, [1,28].”
• Stereographic wavelet frames on the sphere (2005, methodology): “13) The proof of these results and more details on the spherical CWT and its implementation can be found in [5] (see also [7] and [15]).”
• The Monogenic Synchrosqueezed Wavelet Transform: A tool for the Decomposition/Demodulation of AM-FM images (2012, background): “(4) Cψ = (2π) 2 ∫ R2 |ψ̂(ξ)|2 |ξ|2 dξ < +∞ As usual (see [28]), the wavelet family {ψa,α,b}(a,α,b)∈R∗+×(0,2π)×R2 is defined by ψa,α,b = TbRαDaψ.”