On the existence of equiangular tight frames

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Web1 de jul. de 2008 · Yet, despite their importance, we are far from having a complete understanding about the existence of equiangular tight frames. Some results can be … WebThe constructionoftheMercedes–Benz frame, thewell-known example of a tight frame on the plane, is generalized to the space Rn. The existence problems for the …

A note on equiangular tight frames - ScienceDirect

WebComplex Equiangular Tight Frames Joel A. Troppa aMathematics Department, The University of Michigan, 530 Church St., Ann Arbor, MI 48109-1043, USA ... First, one could demonstrate the existence of speciﬁc complex ETFs via constructive (or nonconstructive) means. Second, one could attempt to rule out the possibility that a complex WebThe constructionoftheMercedes–Benz frame, thewell-known example of a tight frame on the plane, is generalized to the space Rn. The existence problems for the Mercedes–Benz systems and other more general equiangular tight frames are discussed. It is shown that the Welch inequality becomes the equality only on equiangular tight frames (if ... dickens hawthorne

Tremain equiangular tight frames - ScienceDirect

WebEquiangular Tight Frames Let {x m} be a collection of N unit vectors in Cd with N ≥ d A lower bound on the maximum correlation between a pair of vectors: max m6= n hx m, x ni ≥ s N −d d(N −1) def= µ(d,N) The bound is met if and only if 1. The vectors are equiangular 2. The vectors form a tight frame http://users.cms.caltech.edu/~jtropp/slides/Tro05-Complex-Equiangular-Talk.pdf WebSequences, or optimal Grassmannian frames, or two-uniform frames. We prefer the more descriptive term “equiangular tight frame.” 1.1 Summary of Results The numerical … dickens heater

[1703.01786] Constructions of biangular tight frames and their ...

WebSequences, or optimal Grassmannian frames, or two-uniform frames. We prefer the more descriptive term “equiangular tight frame.” 1.1 Summary of Results The numerical evidence suggests that ETFs do not arise for most pairs (d,N). See [21, Sec. V-C] for details of this investigation. The goal of the present paper Web26 de fev. de 2024 · Abstract An equiangular tight frame (ETF) is an equal norm tight frame with the same sharp angles between the vectors. This work is an attempt to create a brief review with complete proofs and calculations of two directions of research on the equiangular tight frames (ETF): bounds of the spark of the ETF, namely the smallest … dickens heath car body repairsWeb1 de jan. de 2024 · For every V ≡ 1 or 3 mod 6 with V ≥ 3, there exists an equiangular tight frame of N vectors in C M with M = 1 6 ( V + 2) ( V + 3), N = 1 2 ( V + 1) ( V + 2). As … dickens heath council

"Webd2 and a pair of ETFs (equiangular tight frames) in dimensions d(d± 1)/2. We also show that a WH (Weyl Heisenberg covariant) SIC in odd dimension dis naturally associated to a pair of symmetric tight fusion frames in dimension d. We deduce two relaxations of the WH SIC existence problem. We also ﬁnd a reformulation of the problem in which ... " - On the existence of equiangular tight frames

On the existence of equiangular tight frames

WebAbstract: An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and orthogonal rows of norm sqrt(N/d). Its key property is that the absolute inner … Web12 de abr. de 2024 · Particularly, our choice of spark deficient Gabor frames over other classes of frames that may be spark deficient (e.g. equiangular tight frames ... Data-driven approaches could offer a performance advantage, but they assume the existence of a large training dataset with ground truths, which is not available in all cases; thus, ...

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WebThe Internet Archive offers over 20,000,000 freely downloadable books and texts. There is also a collection of 2.3 million modern eBooks that may be borrowed by anyone with a free archive.org account. Borrow a Book Books on Internet Archive are … Webis an equiangular tight frame for R(M N). We call this the complementary equiangular tight frame. It follows that equiangular tight frames come in pairs and if M>2Nthen M<2(M N). So we only need to classify the equiangular tight frames for M>2N. Certain classes of equiangular tight frames always exist. Proposition 3.3: RN always has an 1.

Web15 de out. de 2007 · We prove the existence of equiangular tight frames having n = 2 d-1 elements drawn from either C d or C d-1 whenever n is either 2 k-1 for k ∈ 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 2 d-element equiangular tight frame based on ... Webtight frame exists for each pair (d,N) with N ≤ 100 that meets the new conditions. The arguments also extend to deliver novel necessary conditions for the existence of equiangular tight frames whose Gram matrices have entries drawn from a discrete set of complex numbers. Index Terms—tight frame, equiangular lines, optimal Grassman-

Web1 de out. de 2007 · Request PDF On the existence of equiangular tight frames An equiangular tight frame (ETF) is a d×N matrix that has unit-norm columns and … Web14 de set. de 2015 · Abstract. 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 ...

Web6 de mar. de 2024 · We also develop a general framework of so-called harmonic BTFs and Steiner BTFs - which includes the equiangular cases, surprisingly, the development of …

Web29 de set. de 2010 · Doubly transitive equiangular tight frames that contain regular simplices. M. Fickus, Evan C. Lake. Mathematics. ArXiv. 2024. An equiangular tight … dickens heath development company limitedWebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): dickens heath curryWeb25 de fev. de 2009 · A survey on equiangular tight frames in the space $$ \\mathbb{R}^n $$ is presented. Several equivalent definitions of a tight frame are given. The … dickens havishamWebis an equiangular tight frame for R(M N). We call this the complementary equiangular tight frame. It follows that equiangular tight frames come in pairs and if M>2Nthen … citizens bank corporate loginWebFinally, we mention a general necessary condition for the existence of equiangular tight frames. Compared to the local conditions described above, it is a global condition depending on solely the parameters n and m. Theorem 2.5 (Naimark, see e.g. [7]). dickens heath floristWeb开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 citizens bank corporate emailWebframes and strongly regular graphs of a certain type, it has been veriﬁed that a real equiangular tight frame exists for each pair (d,N) with N ≤ 100 that meets the new … citizens bank corporate campus johnston ri