Construction of compactly Supported Conjugate Symmetric Complex Tight Wavelet Frames

Compactly Supported Symmetric C∞ Wavelets with Spectral Approximation Order

In this paper, we obtain symmetric C∞ real-valued tight wavelet frames in L2(R) with compact support and the spectral frame approximation order. Furthermore, we present a family of symmetric compactly supported C∞ orthonormal complex wavelets in L2(R). A complete analysis of nonstationary tight wavelet frames and orthonormal wavelet bases in L2(R) is given.

Construction of Multivariate Compactly Supported Tight Wavelet Frames

Two simple constructive methods are presented to compute compactly supported tight wavelet frames for any given refinable function whose mask satisfies the QMF or sub-QMF conditions in the multivariate setting. We use one of our constructive methods in order to find tight wavelet frames associated with multivariate box splines, e.g., bivariate box splines on a three or four directional mesh. Mo...

Symmetric Framelets

We study tight wavelet frames associated with symmetric compactly supported re-nable functions, which are obtained with the unitary extension principle. We give a criterion for existence of two symmetric or antisymmetric compactly supported framelets. All reenable masks of length up to 6, satisfying this criterion, are found.

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Symmetric Mra Tight Wavelet Frames with Three Generators and High Vanishing Moments

Let φ be a compactly supported symmetric real-valued refinable function in L2(R) with a finitely supported symmetric real-valued mask on Z. Under the assumption that the shifts of φ are stable, in this paper we prove that one can always construct three wavelet functions ψ, ψ and ψ such that (i) All the wavelet functions ψ, ψ and ψ are compactly supported, real-valued and finite linear combinati...