Quasi-symmetric designs and equiangular tight frames

Matthew Fickus; John Jasper; Dustin Mixon; Jesse Peterson

doi:10.1117/12.2189347

24 August 2015 Quasi-symmetric designs and equiangular tight frames

Matthew Fickus, John Jasper, Dustin Mixon, Jesse Peterson

Proceedings Volume 9597, Wavelets and Sparsity XVI; 95970F (2015) https://doi.org/10.1117/12.2189347
Event: SPIE Optical Engineering + Applications, 2015, San Diego, California, United States

Abstract

An equiangular tight frame (ETF) is an M×N matrix which has orthogonal equal norm rows, equal norm columns, and the inner products of all pairs of columns have the same modulus. ETFs arise in numerous applications, including compressed sensing. They also seem to be rare: despite over a decade of active research by the community, only a few construction methods have been discovered. In this article we introduce a new construction of ETFs which uses a particular set of combinatorial designs called quasi-symmetric designs. For ETFs whose entries are contained in {+1;-1}, called real constant amplitude ETFs (RCAETFs), we see that this construction is reversible, giving new quasi-symmetric designs from the known constructions RCAETFs.

Citation Download Citation

Matthew Fickus, John Jasper, Dustin Mixon, and Jesse Peterson "Quasi-symmetric designs and equiangular tight frames", Proc. SPIE 9597, Wavelets and Sparsity XVI, 95970F (24 August 2015); https://doi.org/10.1117/12.2189347

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