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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

We introduce a general technique to construct tight fusion frames with prescribed symmetries. Applying this technique with a prescription for "all the symmetries", we construct a new family of equi-isoclinic tight fusion frames (EITFFs),…

Combinatorics · Mathematics 2026-01-23 Matthew Fickus , Joseph W. Iverson , John Jasper , Dustin G. Mixon

Every equi-isoclinic tight fusion frame (EITFF) is a type of optimal code in a Grassmannian, consisting of subspaces of a finite-dimensional Hilbert space for which the smallest principal angle between any pair of them is as large as…

Information Theory · Computer Science 2025-01-29 Matthew Fickus , Enrique Gomez-Leos , Joseph W. Iverson

An equichordal tight fusion frame (ECTFF) is a finite sequence of equi-dimensional subspaces of a finite-dimensional Hilbert space that achieves equality in Conway, Hardin and Sloane's simplex bound. Every ECTFF is a type of optimal…

Functional Analysis · Mathematics 2021-03-05 Matthew Fickus , Benjamin R. Mayo , Cody E. Watson

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

Equi-chordal and equi-isoclinic tight fusion frames (ECTFFs and EITFFs) are both types of optimal packings of subspaces in Euclidean spaces. In the special case where these subspaces are one-dimensional, ECTFFs and EITFFs both correspond to…

Functional Analysis · Mathematics 2017-08-30 Matthew Fickus , John Jasper , Dustin G. Mixon , 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

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 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 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

Configurations of subspaces like equichordal and equiisoclinic tight fusion frames, which are in some sense optimally spread apart and which also have reconstruction properties emulating those of orthonormal bases, are useful in various…

Functional Analysis · Mathematics 2021-05-10 Emily J. King

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

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

An equiangular tight frame (ETF) is a type of optimal packing of lines in a finite-dimensional Hilbert space. ETFs arise in various applications, such as waveform design for wireless communication, compressed sensing, quantum information…

Functional Analysis · Mathematics 2017-07-04 Matthew Fickus , John Jasper , Dustin G. Mixon , Jesse D. Peterson , Cody E. Watson

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

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) 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

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

Equiangular tight frames (ETFs) have found significant applications in signal processing and coding theory due to their robustness to noise and transmission losses. ETFs are characterized by the fact that the coherence between any two…

Information Theory · Computer Science 2018-04-10 Somantika Datta , Jesse Oldroyd

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
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