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Articles 1 - 4 of 4
Full-Text Articles in Harmonic Analysis and Representation
Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Matthew C. Fickus, Courtney A. Schmitt
Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Matthew C. Fickus, Courtney A. Schmitt
Faculty Publications
An equiangular tight frame (ETF) is a sequence of unit-norm vectors in a Euclidean space whose coherence achieves equality in the Welch bound, and thus yields an optimal packing in a projective space. A regular simplex is a simple type of ETF in which the number of vectors is one more than the dimension of the underlying space. More sophisticated examples include harmonic ETFs which equate to difference sets in finite abelian groups. Recently, it was shown that some harmonic ETFs are comprised of regular simplices. In this paper, we continue the investigation into these special harmonic ETFs. We begin …
Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Courtney A. Schmitt
Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Courtney A. Schmitt
Theses and Dissertations
An equiangular tight frame (ETF) is a sequence of equal-norm vectors in a Euclidean space whose coherence achieves equality in the Welch bound, and thus yields an optimal packing in a projective space. A regular simplex is a simple type of ETF in which the number of vectors is one more than the dimension of the underlying space. More sophisticated examples include harmonic ETFs, which are formed by restricting the characters of a finite abelian group to a difference set. Recently, it was shown that some harmonic ETFs are themselves comprised of regular simplices. In this thesis, we continue the …
Parametrizing Finite Frames And Optimal Frame Completions, Miriam J. Poteet
Parametrizing Finite Frames And Optimal Frame Completions, Miriam J. Poteet
Theses and Dissertations
Frames are used in many signal processing applications. We consider the problem of constructing every frame whose frame operator has a given spectrum and whose vectors have prescribed lengths. For a given spectrum and set of lengths, we know when such a frame exists by the Schur-Horn Theorem; it exists if and only if its spectrum majorizes its squared lengths. We provide a more constructive proof of Horn's original result. This proof is based on a new method for constructing any and all frames whose frame operator has a prescribed spectrum and whose vectors have prescribed lengths. Constructing all such …
A Non-Homogeneous, Spatio-Temporal, Wavelet Multiresolution Analysis And Its Application To The Analysis Of Motion, Thomas J. Burns
A Non-Homogeneous, Spatio-Temporal, Wavelet Multiresolution Analysis And Its Application To The Analysis Of Motion, Thomas J. Burns
Theses and Dissertations
This research presents a multiresolution wavelet analysis tool for analyzing motion in time sequential imagery. A theoretical framework is developed for constructing an L2R wavelet multiresolution analysis from three non-identical spatial and temporal L2R wavelet multiresolution analyses. This framework provides the flexibility to tailor the spatio-temporal frequency characteristics of the three dimensional wavelet filter to match the frequency behavior of the analyzed signal. An unconventional, discrete multiresolution wavelet decomposition algorithm is developed which yields a rich set of independent spatio-temporally oriented frequency channels for analyzing, the size and speed characteristics of moving objects. Unlike conventional wavelet decomposition methods, this algorithm …