Riesz wavelets and generalized multiresolution analyses
نویسندگان
چکیده
منابع مشابه
Multiresolution Analyses and Wavelets for Density Estimation
We use the concept of multiresolution analysis and orthonormal basis of wavelet functions to construct an estimator for an unknown density in a given Sobolev’s space. We show consistency with the rate of convergence equal to the optimal minimax rate of convergence. We also discuss some of the features of this new method of estimation on a numerical example.
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We investigate Riesz bases of wavelets generated from multiresolution analysis. This investigation leads us to a study of refinement equations with masks being exponentially decaying sequences. In order to study such refinement equations we introduce the cascade operator and the transition operator. It turns out that the transition operator associated with an exponentially decaying mask is a co...
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Multiresolution is investigated on the basis of shift-invariant spaces. Given a finitely generated shift-invariant subspace S of L2(IR), let Sk be the 2-dilate of S (k ∈ ZZ). A necessary and sufficient condition is given for the sequence {Sk}k∈Z to form a multiresolution of L2(IR). A general construction of orthogonal wavelets is given, but such wavelets might not have certain desirable propert...
متن کاملWavelets and Multiresolution Processing
– Fourier transform used to analyze signals by converting signals into a continuous series of sine and cosine functions, each with a constant frequency and amplitude, and of infinite duration – Real world signals (images) have a finite duration and exhibit abrupt changes in frequency – Wavelet transform converts a signal into a series of wavelets – In theory, signals processed by wavelets can b...
متن کاملWavelets and Multiresolution Processing
– Fourier transform used to analyze signals by converting signals into a continuous series of sine and cosine functions, each with a constant frequency and amplitude, and of infinite duration – Real world signals (images) have a finite duration and exhibit abrupt changes in frequency – Wavelet transform converts a signal into a series of wavelets – In theory, signals processed by wavelets can b...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2003
ISSN: 1063-5203
DOI: 10.1016/s1063-5203(03)00022-8