On Approximation with Wave Packets Generated from a Refinable Function
نویسندگان
چکیده
We consider best m-term approximation in Lp(R) with wave packets generated from a single refinable function. The main examples of such wave packets are orthonormal wavelets or more generally tight wavelet frames based on an MRA (so-called framelets). The approximation classes associated with best m-term approximation in Lp(R) with such wave packets are completely characterized in terms of Besov spaces. As an application of the main result we show that for m-term approximation in Lp(R) with elements from an oversampled version of a framelet system with compactly supported generators, the associated approximation classes turn out to be (essentially) Besov spaces.
منابع مشابه
Approximation with Wave Packets Generated by a Refinable Function
We consider best m-term approximation in Lp(R) with wave packets generated by a single refinable function. The main examples of wave packets are orthonormal wavelets, or more generally wavelet frames based on a multiresolution analysis (so-called framelets). The approximation classes associated with best m-term approximation in Lp(R) for a large class of wave packets are completely characterize...
متن کاملRefinable Subspaces of a Refinable Space
Local refinable finitely generated shift-invariant spaces play a significant role in many areas of approximation theory and geometric design. In this paper we present a new approach to the construction of such spaces. We begin with a refinable function ψ : R → Rm which is supported on [0, 1]. We are interested in spaces generated by a function φ : R → Rn built from the shifts of ψ.
متن کاملApproximation properties of multivariate wavelets
Wavelets are generated from refinable functions by using multiresolution analysis. In this paper we investigate the approximation properties of multivariate refinable functions. We give a characterization for the approximation order provided by a refinable function in terms of the order of the sum rules satisfied by the refinement mask. We connect the approximation properties of a refinable fun...
متن کاملCompactly Supported Multivariate, Pairs of Dual Wavelet Frames Obtained by Convolution
In this paper, we present a construction of compactly supported multivariate pairs of dual wavelet frames. The approach is based on the convolution of two refinable distributions. We obtain smooth wavelets with any preassigned number of vanishing moments. Their underlying refinable function is fundamental. In the examples, we obtain symmetric wavelets with small support from optimal refinable f...
متن کاملApproximation by Multiple Refinable Functions †
We consider the shift-invariant space, S(Φ), generated by a set Φ = {φ1, . . . , φr} of compactly supported distributions on IR when the vector of distributions φ := (φ1, . . . , φr) satisfies a system of refinement equations expressed in matrix form as φ = ∑
متن کامل