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Ten Lectures on Wavelets
TLDR
Introduction Preliminaries and notation The what, why, and how of wavelets The continuous wavelet transform Discrete wavelet transforms: Frames Time-frequency density and orthonormal bases Orthonormal wavelet bases of compactly supported wavelets and multiresolutional analysis. Expand
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Continuous and Discrete Wavelet Transforms
TLDR
This paper is an expository survey of results on integral representations and discrete sum expansions of functions in $L^2 ({\bf R})$ in terms of coherent states. Expand
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The application of multiwavelet filterbanks to image processing
TLDR
Multiwavelets are a new addition to the body of wavelet theory. Expand
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Density, overcompleteness, and localization of frames
This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I andExpand
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THE APPLICATION OF MULTIWAVELET FILTER BANKS TO IMAGE PROCESSING ∗
Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filter banks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and shortExpand
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Matrix Refinement Equations: Existence and Uniqueness
Matrix reenement equations are functional equations of the form f(x) = P N k=0 c k f(2x ? k), where the coeecients c k are matrices and f is a vector-valued function. Reenement equations play keyExpand
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Approximation by translates of refinable functions
Summary. The functions $f_1(x), \dots, f_r(x)$ are refinable if they are combinations of the rescaled and translated functions $f_i(2x-k)$ . This is very common in scientific computing on a regularExpand
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Modulation spaces and pseudodifferential operators
We use methods from time-frequency analysis to study boundedness and traceclass properties of pseudodifferential operators. As natural symbol classes, we use the modulation spaces onR2d, whichExpand
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Linear independence of time-frequency translates
Abstract. The refinement equation φ(t) = ∑N2 k=N1 ck φ(2t − k) plays a key role in wavelet theory and in subdivision schemes in approximation theory. Viewed as an expression of linear dependenceExpand
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Accuracy of Lattice Translates of Several Multidimensional Refinable Functions
Complex-valued functionsf1,?,fronRdarerefinableif they are linear combinations of finitely many of the rescaled and translated functionsfi(Ax?k), where the translateskare taken along aExpand
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