A Wavelet Tour of Signal Processing, 2nd Edition

By Stéphane Mallat. 1999

Subfields: Natural Language Processing, Speech & Audio

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Citations in the corpus

Fully convolutional networks for semantic segmentation (2014, methodology): “(This trick is also used in the algorithme à trous [46], [47] for wavelet transforms and related to the Noble identities [48] from signal processing.”
Nonlocal Image Restoration With Bilateral Variance Estimation: A Low-Rank Approach (2013, background): “Wavelet theory advocates for the importance of modeling transient events [51] because they carry important information.”
Generalized Morse Wavelets as a Superfamily of Analytic Wavelets (2012, methodology): “This limit is identical with the definition of the Shannon wavelet [3, p. 246], corresponding to a sinc function in the time domain (14) The slow time decay of this wavelet, however, is an undesirable property that limits its usefulness.”
Non-local Regularization of Inverse Problems (2008, methodology): “The sparsity energy J , defined in equation (4), using a redundant tight frame of translation invariant 7-9 biorthogonal wavelets {ψm}m, see [39].”
Machine learning in acoustics: Theory and applications. (2019, background): “24,63 Such dictionaries have useful properties, which allow them to obtain acceptable sparse representation performance for a broad range of data.”
Optimal rates of convergence for estimating the null density and proportion of nonnull effects in large-scale multiple testing (2010, background): “Now, by Parseval’s formula [Mallat (1998)], for any integers 0≤m≤ k/2, ∫ x|f2(x)− f1(x)|(2) dx= ∫ |xf2(x)− xf1(x)|(2) dx (6.”
Comparison of multiple linear and nonlinear regression, autoregressive integrated moving average, artificial neural network, and wavelet artificial neural network methods for urban water demand forecasting in Montreal, Canada (2012, methodology): “This is achieved by modifying the wavelet representation to [ Mallat , 1999] j ; k ð t Þ ¼ s where j and k are integers and s 0 > 1 is a ﬁxed dilation step.”
Practical Signal Recovery from Random Projections (2005, methodology): “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).”
Exploiting Structure in Wavelet-Based Bayesian Compressive Sensing (2009, methodology): “A discrete wavelet transform may be implemented via a series of high- and low-pass filters, with decimation performed after each such filtering [1].”
Fully Convolutional Networks for Semantic Segmentation (2017, methodology): “(This trick is also used in the algorithme a trous [46], [47] for wavelet transforms and related to theNoble identities [48] from signal processing.”
Evolution of Image Segmentation using Deep Convolutional Neural Network: A Survey (2020, methodology): “To handle the first problem, the authors have employed ‘atrous’ (with holes) [107] algorithm for efficient dense computation of CNN.”
Identification of Intermittent Electrical and Mechanical Faults in Permanent-Magnet AC Drives Based on Time–Frequency Analysis (2007, methodology): “is used in [20], linear convolution is used here since the signals are not periodic.”
Estimation of the density of regression errors (2005, background): “The reader might notice that this smoothing function is the analog of the famous Wiener filter, and this is the reason why it also can be referred to as a filter; see [29], Chapter 10.”
Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal (2008, methodology): “For example, to represent regular structures with point singularities, a qualiﬁed candidate is the wavelet transform [25][1].”
On Consistency and Sparsity for Principal Components Analysis in High Dimensions (2009, background): “When one-dimensional signals are smooth or have isolated discontinuities (either in the signal or its derivatives), then it can be shown (e.g., Mallat 1999) that the wavelet coefficients decay rapidly with frequency octave away from the discontinuities.”
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.”