A Wavelet Tour of Signal Processing : The Sparse Way

By Stéphane Mallat, Gabriel Peyré. 2008

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Citations in the corpus

Computational Optimal Transport (2018, background): “We refer to [Mallat, 2008] for more details on wavelets.”
Multiscale adjoint waveform tomography for surface and body waves (2015, background): “Readers not familiar with the wavelet transform may wish to consult the early work of Morlet et al. (1982a, 1982b), in this journal, or the textbooks by Daubechies (1992), Strang and Nguyen (1997), Mallat (2008), or Jensen and la Cour-Harbo (2001) before reading on.”
Sparse Principal Component Analysis and Iterative Thresholding (2011, methodology): “Before applying any sparse PCA method, we transform the observed data vectors into the wavelet domain using the Symmlet 8 basis [18], and scale all the observations by σ with σ 2 given in (2.3). b b The multi-resolution plots of wavelet coeﬃcients of the test vectors are shown in Fig.”
Signal and noise separation in prestack seismic data using velocity-dependent seislet transform (2015, background): “which means that all transforms taken together constitute a tight frame with constant N (Mallat, 2009).”
Kronecker Compressive Sensing (2012, unknown): “Kronecker products play a central role in generating wavelet bases for multidimensional signals [29]–[31].”
Parallel Transport Convolution: A New Tool for Convolutional Neural Networks on Manifolds (2018, background): “Convolution is a fundamental mathematical operation that arises in many applications in science and engineering [10, 24].”
Efficient stabilization of crop yield prediction in the Canadian Prairies (2012, background): “Alternative bases and levels of sparsity Because of their widely documented ability to model complex nonlinear signals while maintaining sparsity, we briefly explore wavelet bases as an alternative to principal components (Mallat, 2009).”
Empirical Wavelet Transform (2013, background): “For further details, we refer the reader to the extensive literature about the wavelet theory, see for example [3], [10], [12], [14].”
A Systematic Review of Compressive Sensing: Concepts, Implementations and Applications (2018, unknown): “A good introduction about basis, frames and dictionaries in which the sparsest possible representation of a signal can be obtained, is available in articles [12]–[16].”
Unsupervised Deep Haar Scattering on Graphs (2014, background): “ high pass ﬁlter is g(n) = ( 1)nh(1 n), and P n g(n) = 0. One can prove that W= (H;G) is then an orthogonal operator in Rdand that f˚ J(n k2J); j(n k2j)g 0 k d2 j is a wavelet orthonormal basis of Rd[1]. Haar ﬁlters are simple examples deﬁned by h(n) = 2 1=2((n) + (n 1)) and g(n) = 2 1=2((n) (n 1)).”
A Survey of Sparse Representation: Algorithms and Applications (2015, methodology): “transform domain method [5], or i s devised based on learning, i.”