NDLI: Upper and lower redundancy of finite frames

Content Provider	IEEE Xplore Digital Library
Author	Bodmann, B.G. Casazza, P.G. Kutyniok, G.
Copyright Year	2010
Description	Author affiliation: Institute of Mathematics, University of Osnabrück, 49069, Germany (Kutyniok, G.) \|\| Department of Mathematics, University of Houston, TX 77204, USA (Bodmann, B.G.) \|\| Department of Mathematics, University of Missouri, Columbia, 65211, USA (Casazza, P.G.)
Abstract	The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy for finite frames in a Hilbert space. This motivates a carefully chosen list of desired properties for upper and lower redundancies. The means to achieve these properties is to consider the maximum and minimum of a redundancy function, which is interesting in itself. The redundancy function is defined on the sphere of the Hilbert space and measures the concentration of frame vectors around each point. A complete characterization of functions on the sphere which coincide with a redundancy function for some frame is given. The upper and lower redundancies obtained from this function are shown to satisfy all of the intuitively desirable properties. In addition, the range of values they assume is characterized.
Starting Page	1
Ending Page	6
File Size	340264
Page Count	6
File Format	PDF
ISBN	9781424474165
e-ISBN	9781424474172
DOI	10.1109/CISS.2010.5464807
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-03-17
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Frames Data analysis Terminology Sparse Approximation Erasures Redundancy Quantization Extraterrestrial measurements Mathematics Resilience Computer science Linearly Independent Sets Redundancy Function Spanning Sets Signal processing Hilbert space
Content Type	Text
Resource Type	Article

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