NDLI: Operator-Like Wavelet Bases of $L

Content Provider	Springer Nature Link
Author	Khalidov, Ildar Ward, John Paul Unser, Michael
Copyright Year	2013
Abstract	The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction follows from a stochastic model: signals are tempered distributions such that the application of a whitening (differential) operator results in a realization of a sparse white noise. Using wavelets constructed from these operators, the sparsity of the white noise can be inherited by the wavelet coefficients. In this paper, we specify such wavelets in full generality and determine their properties in terms of the underlying operator.
Ending Page	1322
Page Count	29
Starting Page	1294
File Format	PDF
ISSN	10695869
e-ISSN	15315851
Journal	Journal of Fourier Analysis and Applications
Issue Number	6
Volume Number	19
Language	English
Publisher	Springer US
Publisher Date	2013-11-14
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stochastic differential equations Stochastic partial differential equations Multipliers Signal, Image and Speech Processing Fourier multiplier operators Wavelets and other special systems Abstract Harmonic Analysis Wavelets Mathematical Methods in Physics Fourier Analysis Multiresolution Approximations and Expansions Partial Differential Equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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