NDLI: Tight frames and geometric properties of wavelet sets

Content Provider	Springer Nature Link
Author	Benedetto, John J. Sumetkijakan, Songkiat
Copyright Year	2006
Abstract	A construction for providing single dyadic orthonormal wavelets in Euclidean space ℝd is given. It is called the general neighborhood mapping construction. The fact that one wavelet is sufficient to generate an orthonormal basis for L2(ℝd) is the critical issue. The validity of the construction is proved, and the construction is implemented computationally to provide a host of examples illustrating various geometrical properties of such wavelets in the spectral domain. Because of the inherent complexity of these single orthonormal wavelets, the method is applied to the construction of single dyadic tight frame wavelets, and these tight frame wavelets can be surprisingly simple in nature. The structure of the spectral domains of the wavelets arising from the general neighborhood mapping construction raises a basic geometrical question. There is also the question of whether or not the general neighborhood mapping construction gives rise to all single dyadic orthonormal wavelets. Results are proved giving partial answers to both of these questions.
Starting Page	35
Ending Page	56
Page Count	22
File Format	PDF
ISSN	10197168
Journal	Advances in Computational Mathematics
Volume Number	24
Issue Number	1-4
e-ISSN	15729044
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2006-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	frames wavelets Theory of Computation Numeric Computing Mathematics Algebra Calculus of Variations and Optimal Control Optimization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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