Ten Lectures on Wavelets

By Ingrid Daubechies. 1992

Subfields: Numerical Methods & Scientific Computing, Signal Processing

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Citations in the corpus

Wavelets on Graphs via Spectral Graph Theory (2009, neutral): “A more complete discussion of frame theory may be found in [43] and [44].”
Filters, Random Fields and Maximum Entropy (FRAME): Towards a Unified Theory for Texture Modeling (1998, methodology): “For example, we can use both linearand nonlinear lters, and the lters can be highly correlated to each other, whereas in the ltering method, a major concern is whether the lters form a tight frame (Daubechies1992).”
PDE-Net: Learning PDEs from Data (2017, background): “Note that the order of sum rules is closely related to the order of vanishing moments in wavelet theory (Daubechies, 1992; Mallat, 1999).”
VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES OF INTEGRABLE FUNCTIONS AND MERCER THEOREM (2006, background): “In recent years there is a new interest for the theory of RKH spaces in different frameworks, like quantum mechanics [7], signal analysis [8, 6], probability theory [9] and statistical learning theory [10, 11].”
Wavelet Scattering Regression of Quantum Chemical Energies (2016, background): “Such homogeneous singular operators are better represented with wavelet transforms [15, 33, 34, 30].”
Uncertainty Principles and Vector Quantization (2006, positive): “When , the tight frames are linearly dependent systems, so various coefficients of the frame representation may carry common information about vector This makes frames withstand noise in coefficients better than orthonormal bases, see [10], [11], [21].”
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 [1, 2].”
Wavelet Convolutions for Large Receptive Fields (2024, methodology): “Our proposed approach leverages the Wavelet Transform (WT) [9], an established tool from time-frequency analysis, to make the receptive field of convolu-tions scale up well and, by cascading, also guide the CNNs to better respond to low frequencies.”
Non-parametric seismic data recovery with curvelet frames (2008, background): “This `2 optimization problem permits an explicit solution that reads x̃ = A†y := AT ( AAT )−1 y (6) with A† the dual frame (see e.g. Daubechies, 1992; Mallat, 1997), given by the pseudoinverse of A.”
Density, overcompleteness, and localization of frames (2006, methodology): “We use standard notations for frames and Riesz bases as found in the texts [Chr03], [ Dau92 ], [Gr o01], [You01].”
Highly sparse representations from dictionaries are unique and independent of the sparseness measure (2007, unknown): “Many classical frames which come up in signal and image processing, such as Gabor frames [30] and wavelet frames [6, 35, 40, 39, 7, 5] are localized in the above sense, with B a Wilson or a wavelet basis.”
Changes in variance and correlation of soil properties with scale and location: analysis using an adapted maximal overlap discrete wavelet transform (2001, background): “…norm of 1, i.e. j x j2 dx 1; 3 and that this property is retained for all dilations of the mother wavelet: k ;x k2 j ;x w j2 dw j x j2 dx 1: 4 If the mother wavelet satis®es certain additional conditions (see Daubechies, 1992) then the DWT partitions the variance of a signal over all scales.”
Optimally Sparse Multidimensional Representation Using Shearlets (2007, methodology): “In addition, the Multiresolution Analysis (MRA) associated with wavelets provides very fast numerical algorithms for computing the wavelet coe‐cients [ 10 , 28].”