On the existence of equiangular tight frames

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Web3 Real equiangular tight frames In this section, we describe what is known about real equiangular tight frames. Throughout, we use ∃RETF(M,N) to denote the statement “there exists a real equiangular tight frame with parameters (M,N).” We start with some basic properties: Theorem 1 (see [39]). ∃RETF(M,N) implies each of the following: WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda):

A note on equiangular tight frames - ScienceDirect

Web26 de fev. de 2014 · The problem of constructing maximal equiangular tight frames or SICs was raised by Zauner in 1998. Four years ago it was realized that the problem is closely connected to a major open problem in ... 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, ... how much is msc drink package

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

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 … 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 … WebFinally, 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]). how do i change the layout of outlook email

All complex equiangular tight frames in dimension 3

Equiangular tight frames Request PDF - ResearchGate

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 … 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. how much is ms windows 10Webconstruction of equiangular tight frames for ﬁnite dimensional real Hilbert spaces [21, 18, 8, 3, 10], relatively few means are known for constructing equiangular frames in the complex case (see, e.g. [11, 17, 7]). The problem of the existence of equiangular frames is known to be equivalent how much is msft paying for atvi

"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 … " - On the existence of equiangular tight frames

On the existence of equiangular tight frames

WebIt is shown that the existence of frames and duals that attain the lower bound is related to the existence of equiangular tight frames (ETFs). Second, motivated by the scarcity of ETFs (which by default have dual ETFs), we examine the more general question of existence of equiangular frames that have equiangular duals. Web9 de abr. de 2024 · a so-called equiangular tight frame if and only if this lower. bound is saturated, meaning in particular that the subnor-malised projectors {d. n ... deciding the existence of EAMs (see e.g. [68 ...

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WebAn equiangular tight frame (ETF) is a d ×N matrix that has unit-norm columns and orthogonal rows of norm √ … WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and …

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 … Web1 de abr. de 2015 · Tables of the existence of equiangular tight frames. A Grassmannian frame is a collection of unit vectors which are optimally incoherent. To date, the vast …

WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In a recent paper, Holmes and Paulsen established a necessary condition for the existence of an N … Web1 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 illustrated by Tremain's original example above, this construction is real whenever the unimodular simplices come from real Hadamard matrices. In particular, a ( V + 1) × ( V + …

Webframes 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 …

WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and … how much is mschf boxWeb25 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 … how do i change the letter size on my screenWebEquiangular 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 how do i change the look of a desktop iconWebThe 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 … how much is msft worthWebis 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 … how much is msg networkWeb1 de mar. de 2009 · 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 ... how do i change the look of my outlook emailWeb15 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 ... how much is msnbc paying jen psaki