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Wavelets and the theory of non-parametric function estimation
Pinsker’s theorem sparsity statistical decision problem
2015/8/20
Non-parametric function estimation aims to estimate or recover or denoise a function
of interest, perhaps a signal, spectrum or image, that is observed in noise and possibly
indirectly after some tr...
Nonstationary Wavelets Related to the Walsh Functions
Walsh Functions Nonstationary Dyadic Wavelets Fractal Functions Adapted Multiresolution Analysis
2013/1/30
Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line. The masks of these wavelets are the Walsh polynomials defined ...
On the Hilbert transform of wavelets
Hilbert transform wavelets localization vanishing moments
2011/9/19
Abstract: A wavelet is a localized function having a prescribed number of vanishing moments. In this correspondence, we provide precise arguments as to why the Hilbert transform of a wavelet is again ...
Constructing pairs of dual bandlimited frame wavelets in $L^2(\mathbb{R}^n)$
real and expansive dilation matrix bandlimited wavelets dual frames
2010/12/10
Given a real, expansive dilation matrix we prove that any bandlimited function ∈ L2(Rn), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for cer...
Wavelets and framelets from dual pseudo splines
Dual pseudo splines Riesz wavelet basis Tight wavelet frame.
2018/4/19
Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples, which was introduced in [8]. In this paper, we shall construct Riesz wavelet associated with dual ...
Legendre multi-wavelets direct method for linear integro-differential equations
Integro-differential equation Legendre multi-wavelets
2010/9/13
We use the continuous Legendre multi-wavelets on the interval [0, 1) to solve the linear integro-differential equation. To do so, we reduced the problem into a system of algebraic equations. Illustrat...
MORE GENERAL CONSTRUCTIONS OF WAVELETS ON THE INTERVAL
multiresolution analysis wavelet Sobolev space
2008/11/26
In this paper we present general constructions of orthogonal and biorthogonal multiresolution
analysis on the interval. In the first one, we describe a direct method to
define an orthonormal multire...
A CHARACTERIZATION OF GENERALIZED FRAME MRAs DERIVING ORTHONORMAL WAVELETS
orthonormal wavelets generalized frame MRA non-MRA wavelets
2007/12/12
In 2000, Papadakis announced that any orthonormal wavelet must be derived by a generalized frame MRA (GFMRA). In this paper, we give a characterization of GFMRAs which can derive orthonormal wavelets,...
Frame wavelets with compact support for $L^2(R^n)$
Fourier transform frame wavelet expansive matrix
2007/12/11
The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For...
Given a multiresolution analysis of multidimension, we construct pre-wavelets and a Rieszwavelet basis under some assumptions on the scale function. Example are provided.