Joachim Stöckler

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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 N m. Tight frames are also extended to " sibling frames " to(More)
We study Sobolev type estimates for the approximation order resulting from using strictly positive deenite kernels to do interpolation on the n-sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger 10] and related estimates of 6]. These error estimates are then based on series expansions of(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)
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)
1 Abstract. From the definition of tight frames, normalized with frame bound constant equal to one, a tight frame of wavelets can be considered as a natural generalization of an or-thonormal wavelet basis, with the only exception that the wavelets are not required to have norm equal to one. However, without the orthogonality property, the tight-frame(More)
When a Cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L 2 = L 2 (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(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)
where g ∈ L 2 (R) and M lβ T kα g(x) = e 2πilβx g(x − kα). In collaboration with K. Gröchenig, we proved that G(g, α, β) is a frame if αβ < 1 and g is a totally positive function of finite type, i.e., its Fourier transform is g(ω) = C m j=1 (1 + 2πiδ j ω) −1 , δ j ∈ R \ {0}. With T. Kloos from Dortmund, we found new properties of these frames: 1. The Zak(More)