A Theory for Multiresolution Signal Decomposition: The Wavelet Representation

By Stéphane Mallat. 1989

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Speech & Audio

Citations in the corpus

Scattering Networks for Hybrid Representation Learning (2018, background): “A wavelet is an integrable function with zero mean, which is localized both in Fourier and space domain [37].”
Sparse coding with an overcomplete basis set: a strategy employed by V1? (1997, methodology): “the basis of coding strategies such as the Discrete Cosine Transform (used in JPEG image compression), or orthonormal wavelet transforms (Mallat, 1989).”
Deep Image Prior (2017, background): “The statistics of responses to various non-random filters (such as simple operators and higher-order wavelets) have been studied in seminalworks (Field 1987;Mallat 1989; Simoncelli and Adelson 1996; Zhu and Mumford 1997).”
Real-Time Adaptive Image Compression (2017, methodology): “Our pyramidal decomposition encoder is loosely inspired by the use of wavelets for multiresolution analysis, in which an input is analyzed recursively via feature extraction and downsampling operators (Mallat, 1989).”
A Wavelet-Chaos Methodology for Analysis of EEGs and EEG Subbands to Detect Seizure and Epilepsy (2007, methodology): “Wavelet transform uses a variable window size over the length of the signal, which allows the wavelet to be stretched or compressed depending on the frequency of the signal [2], [18], [27].”
Real harmonizable multifractional Lévy motions (2004, background): “Their fields remain lass Gaussian fields, like those studied in Nevertheless in practice, one often observes non-Gaussian phenomena, see for instance [11,16] for image and thus can not use these models.”
Using unlabelled data to update classification rules with applications in food authenticity studies (2006, methodology): “One requirement for the pyramidal algorithm (Mallat, 1989) for completing the discrete wavelet transform is that the length of the data vector must be a power of 2.”
The Cospectral Gap and Turbulent Flux Calculations (2003, methodology): “E-mail: vickers@coas.oregonstate.edu unweighted moving averages (the approach presented here), (ii) the Haar transform method (Haar 1910; Howell and Mahrt 1997), and (iii) wavelets (Mallat 1989; Katul and Vidakovic 1996).”
A Survey on Wind Turbine Condition Monitoring and Fault Diagnosis—Part II: Signals and Signal Processing Methods (2015, background): “In this way, the wavelet transform is capable of grasping both the time and frequency information of a signal [42], [67], [68] and resolving signal denoising problems effectively [6].”
Water levels measured with SNR using wavelet decomposition and Lomb–Scargle periodogram (2017, methodology): “With multiresolution analysis, Mallat (1989) has shown that a linear combination of wavelet dilations and translations forms an orthogonal basis of the set of squared integrable functions: L(2)(R)(2) .”
Implementation of Karhunen-Loeve expansion for simulation using a wavelet-Galerkin scheme (2002, background): “Keywords: Karhunen–Loeve expansion; simulation; Fredholm integral equation; Wavelet-Galerkin; Discrete wavelet transform; Mallat’s tree algorithm; Harr wavelets”
Multi-scale proper orthogonal decomposition of complex fluid flows (2018, methodology): “For the purposes of this work, it suffices to notice that the MRA of K can by carried out via Wavelet toolboxes for image compression/denoising (Gonzalez & Woods 2007; Mallat 2009), based on the pyramid algorithm proposed by Mallat (1989).”