Results 91 to 100 of about 909 (114)

Kirkman Equiangular Tight Frames and Codes [PDF]

IEEE Transactions on Information Theory, 2014
An equiangular tight frame (ETF) is a set of unit vectors in a Euclidean space whose coherence is as small as possible, equaling the Welch bound. Also known as Welch-bound-equality sequences, such frames arise in various applications, such as waveform design and compressed sensing.
John Jasper, Dustin G Mixon, Matthew Fickus   +2 more
exaly   +3 more sources

Equiangular tight frames

Journal of Mathematical Sciences, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A B Pevnyi
exaly   +2 more sources

Equiangular tight frames from Paley tournaments

Linear Algebra and Its Applications, 2007
We prove the existence of equiangular tight frames having n=2d-1 elements drawn from either C^d or C^(d-1) whenever n is either 2^k-1 for k in N, or a power of a prime such that n=3 mod 4. We also find a simple explicit expression for the prime power case by establishing a connection to a 2d-element equiangular tight frame based on quadratic residues.
Joseph M RenéS
exaly   +4 more sources

Constructions of equiangular tight frames with Genetic Algorithms

2009 IEEE International Conference on Systems, Man and Cybernetics, 2009
Equiangular tight frames have applications in communications, signal processing, and coding theory. Previous work demonstrates that few real equiangular tight frames exist for most pairs (n,d), where the frame Φ n d is a d × n matrix with d ≤ n. This work proposes a genetic algorithm as a solution to the frame design problem.
Jason C Isaacs
exaly   +2 more sources

Equiangular tight frame fingerprinting codes

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2011
We show that equiangular tight frames (ETFs) are particularly well suited as additive fingerprint designs against Gaussian averaging collusion attacks when the number of users is less than the square of the signal dimension. The detector performs a binary hypothesis test in order to decide whether a user of interest is among the colluders.
Dustin G. Mixon, Christopher J. Quinn, Negar Kiyavash, Matthew Fickus   +3 more
openaire   +1 more source

Stochastic constructions of equiangular tight frames

2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE), 2011
Equiangular tight frames have applications in communications, signal processing, and coding theory. Previous work demonstrates that few real equiangular tight frames exist for most pairs (n,d). This work compares three stochastic solutions to the frame design problem, specifically, the problem of designing real equiangular tight frames by minimizing ...
Jason C Isaacs
exaly   +2 more sources

Tight frames over the quaternions and equiangular lines

Advances in Computational Mathematics
We show that much of the theory of finite tight frames can be generalised to vector spaces over the quaternions. This includes the variational characterisation, group frames, and the characterisations of projective and unitary equivalence. We are particularly interested in sets of equiangular lines (equi-isoclinic subspaces) and the groups associated ...
Shayne Waldron
exaly   +3 more sources

Complex equiangular tight frames

SPIE Proceedings, 2005
A complex equiangular tight frame (ETF) is a tight frame consisting of N unit vectors in C d whose absolute inner products are identical. One may view complex ETFs as a natural geometric generalization of an orthonormal basis. Numerical evidence suggests that these objects do not arise for most pairs ( d , N).
Joel A Tropp
exaly   +2 more sources

Equiangular tight frames and signature sets in groups

Linear Algebra and Its Applications, 2010
Equiangular tight frames play an important role in several areas of mathematics ranging from signal processing to quantum computing. These are an important class of finite dimensional frames because of their superior performance and numerous applications. In this paper the author presents a novel way to construct equiangular tight frames by considering
exaly   +2 more sources

2- and 3-Covariant Equiangular Tight Frames [PDF]

2019 13th International conference on Sampling Theory and Applications (SampTA), 2019
Equiangular tight frames (ETFs) are configurations of vectors which are optimally geometrically spread apart and provide resolutions of the identity. Many known constructions of ETFs are group covariant, meaning they result from the action of a group on a vector, like all known constructions of symmetric, informationally complete, positive operator ...
Emily J King
exaly   +3 more sources