2007
DOI: 10.1155/2007/27427
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Construction of Orthonormal Piecewise Polynomial Scaling and Wavelet Bases on Non-Equally Spaced Knots

Abstract: This paper investigates the mathematical framework of multiresolution analysis based on irregularly spaced knots sequence. Our presentation is based on the construction of nested nonuniform spline multiresolution spaces. From these spaces, we present the construction of orthonormal scaling and wavelet basis functions on bounded intervals. For any arbitrary degree of the spline function, we provide an explicit generalization allowing the construction of the scaling and wavelet bases on the nontraditional sequen… Show more

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Cited by 2 publications
(5 citation statements)
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“…Before presenting the new basis orthonormalization procedure, Section 2.3 summarizes the previous procedure described in [20] and points out some weaknesses of the resulting scaling and wavelet functions.…”
Section: Multiresolution Analysis Conceptsmentioning
confidence: 99%
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“…Before presenting the new basis orthonormalization procedure, Section 2.3 summarizes the previous procedure described in [20] and points out some weaknesses of the resulting scaling and wavelet functions.…”
Section: Multiresolution Analysis Conceptsmentioning
confidence: 99%
“…In the previous orthonormalization procedure provided in [20], the classical Gram-Schmidt method has been applied to orthonormalize the nonuniform spline basis of the basic spline space S d 0 [I 0,i ], separately on each bounded interval I 0,i . A large family of orthonormal spline scaling basis can be constructed since the Gram-Schmidt method allows us to choose various functions as the reference one, thus generating several bases.…”
Section: Review Of the Previous Orthonormalization Procedurementioning
confidence: 99%
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