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An equiangular tight frame (ETF) is a type of optimal packing of lines in a real or complex Hilbert space. In the complex case, the existence of an ETF of a given size remains an open problem in many cases. In this paper, we observe that…

Functional Analysis · Mathematics 2018-03-21 Matthew Fickus , John Jasper

An equiangular tight frame (ETF) is a type of optimal packing of lines in Euclidean space. A regular simplex is a special type of ETF in which the number of vectors is one more than the dimension of the space they span. In this paper, we…

Functional Analysis · Mathematics 2017-11-21 Matthew Fickus , John Jasper , Emily J. King , Dustin G. Mixon

An equiangular tight frame (ETF) yields a type of optimal packing of lines in a Euclidean space. ETFs seem to be rare, and all known infinite families of them arise from some type of combinatorial design. In this paper, we introduce a new…

Functional Analysis · Mathematics 2020-01-08 Matthew Fickus , Benjamin R. Mayo

An equiangular tight frame (ETF) is a set of equal norm 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,…

Functional Analysis · Mathematics 2016-06-24 Matthew Fickus , Dustin G. Mixon , John Jasper

An equiangular tight frame (ETF) is a type of optimal packing of lines in Euclidean space. They are often represented as the columns of a short, fat matrix. In certain applications we want this matrix to be flat, that is, have the property…

Functional Analysis · Mathematics 2017-03-17 Matthew Fickus , John Jasper , Dustin G. Mixon , Jesse D. Peterson

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…

Functional Analysis · Mathematics 2019-10-07 Matthew Fickus , Courtney A. Schmitt

An equiangular tight frame (ETF) is a sequence of vectors in a Hilbert space that achieves equality in the Welch bound and so has minimal coherence. More generally, an equichordal tight fusion frame (ECTFF) is a sequence of equi-dimensional…

Functional Analysis · Mathematics 2021-05-11 Matthew Fickus , Joseph W. Iverson , John Jasper , Emily J. King

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…

Group Theory · Mathematics 2019-05-22 Emily J. King

In this paper we describe some new algebraic features of the Gram matrices of complex Equiangular Tight Frames (ETF). This lead on the one hand to the nonexistence of several low dimensional complex ETFs; and on the other hand to the full…

Functional Analysis · Mathematics 2014-02-27 Ferenc Szöllősi

Frame theory is a powerful tool in the domain of signal processing and communication. Among its numerous configurations, the ones which have drawn much attention recently are Equiangular Tight Frame (ETF) and Grassmannian Frame. These…

Information Theory · Computer Science 2013-07-02 Hailong Shi , Hao Zhang

Equiangular tight frames (ETFs) may be used to construct examples of feasible points for semidefinite programs arising in sum-of-squares (SOS) optimization. We show how generalizing the calculations in a recent work of the authors' that…

Functional Analysis · Mathematics 2019-01-31 Afonso S. Bandeira , Dmitriy Kunisky

An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. They arise in numerous applications. It is well known that real ETFs are equivalent to a certain…

Functional Analysis · Mathematics 2016-01-20 Matthew Fickus , Cody E. Watson

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…

Information Theory · Computer Science 2013-06-14 John Jasper , Dustin G. Mixon , Matthew Fickus

Frames have become standard tools in signal processing due to their robustness to transmission errors and their resilience to noise. Equiangular tight frames (ETFs) are particularly useful and have been shown to be optimal for transmission…

Information Theory · Computer Science 2016-12-06 Somantika Datta , Jesse Oldroyd

An equiangular tight frame (ETF) is a finite sequence of equal norm vectors in a Hilbert space that achieves equality in the Welch bound, and so has minimal coherence. The binder of an ETF is the set of all subsets of its indices whose…

Functional Analysis · Mathematics 2025-07-22 Matthew Fickus , Evan C. Lake

A Grassmannian frame is a collection of unit vectors which are optimally incoherent. To date, the vast majority of explicit Grassmannian frames are equiangular tight frames (ETFs). This paper surveys every known construction of ETFs and…

Functional Analysis · Mathematics 2016-06-17 Matthew Fickus , Dustin G. Mixon

An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. Though they arise in many applications, only a few methods for constructing them are known. Motivated…

Functional Analysis · Mathematics 2016-06-21 Matthew Fickus , John Jasper , Dustin G. Mixon , Jesse D. Peterson , Cody E. Watson

Equiangular tight frames (ETFs) and biangular tight frames (BTFs) - sets of unit vectors with basis-like properties whose pairwise absolute inner products admit exactly one or two values, respectively - are useful for many applications. A…

Functional Analysis · Mathematics 2017-07-07 Peter G. Casazza , Amineh Farzannia , John I. Haas , Tin T. Tran

We study several interesting examples of Biangular Tight Frames (BTFs) - basis-like sets of unit vectors admitting exactly two distinct frame angles (ie, pairwise absolute inner products) - and examine their relationships with Equiangular…

Functional Analysis · Mathematics 2017-03-17 John I. Haas , Jameson Cahill , Janet Tremain , Peter G. Casazza

An equi-isoclinic tight fusion frame (EITFF) is a type of Grassmannian code, being a sequence of subspaces of a finite-dimensional Hilbert space of a given dimension with the property that the smallest spectral distance between any pair of…

Information Theory · Computer Science 2021-12-30 Matthew Fickus , Joseph W. Iverson , John Jasper , Dustin G. Mixon
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