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Diagram vectors and tight frame scaling in finite dimensions

2014; University of Zagreb; Issue: 1 Linguagem: Inglês

10.7153/oam-08-02

1848-9974

Martin S. Copenhaver, Yeon Hyang Kim, Cortney Logan, Kyanne Mayfield, Sivaram K. Narayan, Matthew J. Petro, Jonathan Sheperd,

Medical Image Segmentation Techniques

We consider frames in a finite-dimensional Hilbert space H n where frames are exactly the spanning sets of the vector space.The diagram vector of a vector in R 2 was previously defined using polar coordinates and was used to characterize tight frames in R 2 in a geometric fashion.Reformulating the definition of a diagram vector in R 2 we provide a natural extension of this notion to R n and C n .Using the diagram vectors we give a characterization of tight frames in R n or C n .Further we provide a characterization of when a unit-norm frame in R n or C n can be scaled to a tight frame.This classification allows us to determine all scaling coefficients that make a unit-norm frame into a tight frame.