On the existence of equiangular tight frames
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 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
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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 … Web25 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 …
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- WebA Grassmannian frame is a collection of unit vectors which are optimally incoherent. The most accessible (and perhaps most beautiful) of Grassmannian frames are equiangular tight frames (ETFs); indeed, there are infinite families of known ETFs, whereas only finitely many non-ETF Grassmannianframesare knownto date.
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 … Web6 de ago. de 2012 · An equiangular tight frame (ETF) is a d * n matrix that has orthogonal rows and unit-norm columns. ETFs have applications in communications, coding theory and quantum computing.
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]).
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 … hennepin women correctional facilityWeb15 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 ... hennepin whole foodsWeb12 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, ... hennepin workforce leadership councilWebThe constructionoftheMercedes–Benz frame, thewell-known example of a tight frame on the plane, is generalized to the space Rn. The existence problems for the … lars olander revision abWeb29 de set. de 2010 · Doubly transitive equiangular tight frames that contain regular simplices. M. Fickus, Evan C. Lake. Mathematics. ArXiv. 2024. An equiangular tight … lars mousingWeb14 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 ... hennepin weatherWeb4 de ago. de 2015 · Neither the existence of SIC-POVMs in higher-dimensional Hilbert spaces nor the nonexistence of MUBs in a six-dimensional Hilbert space has been proved. On the other hand, conditional SIC-POVMs are considered as equiangular tight frames. The existence of equiangular tight frames is also studied in many literature (e.g., [8, … hennepin waste drop off