30 August 2005 Complex equiangular tight frames
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Proceedings Volume 5914, Wavelets XI; 591401 (2005) https://doi.org/10.1117/12.618821
Event: Optics and Photonics 2005, 2005, San Diego, California, United States
Abstract
A complex equiangular tight frame (ETF) is a tight frame consisting of N unit vectors in Cd 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). The goal of this paper is to develop conditions on (d, N) under which complex ETFs can exist. In particular, this work concentrates on the class of harmonic ETFs, in which the components of the frame vectors are roots of unity. In this case, it is possible to leverage field theory to obtain stringent restrictions on the possible values for (d, N).
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Joel A. Tropp, Joel A. Tropp, } "Complex equiangular tight frames", Proc. SPIE 5914, Wavelets XI, 591401 (30 August 2005); doi: 10.1117/12.618821; https://doi.org/10.1117/12.618821
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