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The notion of vanishing-moment recovery (VMR) functions is introduced in this paper for the construction of compactly supported tight frames with two generators having the maximum order of vanishing moments as determined by the given refinable function, such as the mth order cardinal B-spline Nm. Tight frames are also extended to “sibling frames” to allow… (More)

This paper uses the UEP approach for the construction of wavelet tight frames with two (anti-) symmetric wavelets, and provides some results and examples that complement recent results by Q. Jiang. A description of a family of solutions when the lowpass scaling filter is of even-length is provided. When one wavelet is symmetric and the other is… (More)

- Kurt Jetter, Joachim Stöckler, Joseph D. Ward
- Math. Comput.
- 1999

We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the n-sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger and related estimates. These error estimates are then based on series expansions of smooth… (More)

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… (More)

The notion of tight (wavelet) frames could be viewed as a generalization of orthonormal wavelets. By allowing redundancy, we gain the necessary flexibility to achieve such properties as “symmetry” for compactly supported wavelets and, more importantly, to be able to extend the classical theory of spline functions with arbitrary knots to a new theory of… (More)

Our goal is to present a systematic algorithm for constructing (anti)symmetric tight wavelet frames and orthonormal wavelet bases generated by a given refinable function with an integer dilation factor d 2. Special attention is paid to the issues of the minimality of a number of framelet generators and the size of generator supports. In particular, our… (More)

An important tool for the construction of tight wavelet frames is the Unitary Extension Principle first formulated in the Fourierdomain by Ron and Shen. We show that the time-domain analogue of this principle provides a unified approach to the construction of tight frames based on many variations of multiresolution analyses, e.g., regular refinements of… (More)

- Kurt Jetter, Joachim Stöckler
- Computer Aided Geometric Design
- 2003

- Severin Bannert, Karlheinz Gröchenig, Joachim Stöckler
- IEEE Transactions on Information Theory
- 2014

In this paper, a large class of universal windows for Gabor frames (Weyl-Heisenberg frames) is constructed. These windows have the fundamental property that every overcritical rectangular lattice generates a Gabor frame. Likewise, every undercritical rectangular lattice generates a Riesz sequence.

- Charles K. Chui, Wenjie He, Joachim Stöckler, Qiyu Sun
- Adv. Comput. Math.
- 2003

When a Cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L = L(IR) with dilation integer factor M ≥ 2, the standard “matrix extension” approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any… (More)