Construction of Multivariate Tight Frames via Kronecker Products

Charles K. Chui; Wenjie He

doi:10.1006/acha.2001.0355

Construction of Multivariate Tight Frames via Kronecker Products

Charles K. Chui, Wenjie He

University of Missouri-St. Louis

Research output: Contribution to journal › Article › peer-review

Abstract

Integer-translates of compactly supported univariate refinable functions φi, such as cardinal B-splines, have been used extensively in computational mathematics. Using certain appropriate direction vectors, the notion of (multivariate) box splines can be generalized to (non-tensor-product) compactly supported multivariate refinable functions from the φi’s. The objective of this paper is to introduce a Kronecker-product approach to build compactly supported tight frames associated with , using the two-scale symbols of the univariate tight frame generators

associated with the φi’s.

Original language	American English
Journal	Applied and Computational Harmonic Analysis
Volume	11
DOIs	https://doi.org/10.1006/acha.2001.0355
State	Published - Jan 9 2001

Disciplines

Mathematics
Analysis
Discrete Mathematics and Combinatorics

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Cite this

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abstract = " Integer-translates of compactly supported univariate refinable functions φi, such as cardinal B-splines, have been used extensively in computational mathematics. Using certain appropriate direction vectors, the notion of (multivariate) box splines can be generalized to (non-tensor-product) compactly supported multivariate refinable functions from the φi{\textquoteright}s. The objective of this paper is to introduce a Kronecker-product approach to build compactly supported tight frames associated with , using the two-scale symbols of the univariate tight frame generators associated with the φi{\textquoteright}s.",

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AB - Integer-translates of compactly supported univariate refinable functions φi, such as cardinal B-splines, have been used extensively in computational mathematics. Using certain appropriate direction vectors, the notion of (multivariate) box splines can be generalized to (non-tensor-product) compactly supported multivariate refinable functions from the φi’s. The objective of this paper is to introduce a Kronecker-product approach to build compactly supported tight frames associated with , using the two-scale symbols of the univariate tight frame generators associated with the φi’s.

UR - http://www.umsl.edu/mathcs/about/People/Faculty/WenjieHe/He%20he%20Wen/construction%20of%20multivariate.pdf

U2 - 10.1006/acha.2001.0355

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M3 - Article

VL - 11

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

ER -

Construction of Multivariate Tight Frames via Kronecker Products

Abstract

Disciplines

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