Equiangular tight frames

Journal of Mathematical Sciences

Volumn 157, Issue 6, 2009, Pages 789-815

  Malozemov, V N ^a   Pevnyi, A B ^b  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b SYKTYVKAR STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 61449215007     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/s10958-009-9366-6     Document Type: Article

References (37)

1. J. Kovačevič and A. Chebira, "Life beyond bases: the advent of frames. Part 1," IEEE Signal Process. Magazine, July 2007, 86-114.
2. J. Kovačevič and A. Chebira, "Life beyond bases: the advent of frames. Part 2," IEEE Signal Process. Magazine, September 2007, 115-125.
3. P. G. Casazza, D. Redmond, and J. C. Tremain, "Real equiangular frames." ( http://www.math.missouri.edu/pete )
4. P Casazza J Kovačevič 2003 Equal-norm tight frames with erasures Adv. Comp. Math. 18 2-4 387 430
5. VK Goyal J Kovačevič JA Kelner 2001 Quantized frame expansions with erasures Appl. Comput. Harmonic Anal. 10 3 203 233
6. JJ Benedetto M Fickus 2003 Finite normalized tight frames. Frame potentials Adv. Comput. Math. 18 2-4 357 385
7. PG Casazza 2004 Custom building finite frames Contemporary Math. 345 61 86
8. I. Daubechies, Ten Lectures on Wavelets, Philadelphia (1992).
9. P Delsarte JM Goetals JJ Seidel 1975 Bounds for systems of lines and Jacobi polynomials Philips Res. Repts. 30 3 91 105
10. PWH Lemmens JJ Seidel 1973 Equiangular lines J. Algebra 24 3 494 512
11. LR Welch 1974 Lower bounds on the maximum cross-correlation of signals IEEE Trans. Inf. Theory 20 397 399
12. T Strohmer RW Heath 2003 Grassmannian frames with applications to coding and communication Appl. Comput. Harmonic Anal. 14 3 257 275
13. RB Holmes VI Paulsen 2004 Optimal frames for erasures Linear Algebra Appl. 377 31 51
14. A. M. Duryagin and A. B. Pevnyi, "Grassmannian frames" [in Russian], Workshop DHA & CAGD. Selected Topics. 4 November 2007. ( http://dha.spb.ru/reps07.shtml#1104 ).
15. V. V. Maximenko and A. B. Pevnyi, "Existence of equiangular tight frames" [in Russian], Workshop DHA & CAGD. Selected Topics. 26 March 2008. ( http://dha.spb.ru/reps08.shtml#0326 ).
16. V. N. Malozemov and A. B. Pevnyi, "Mercedes-Benz Systems and tight frames" [in Russian], Workshop DHA & CAGD. Selected Topics. 28 February 2007. ( http://dha.spb.ru/reps07.shtml#0228 ).
17. V. N. Malozemov and A. B. Pevnyi, "Equiangular systems of vectors and tight frames" [in Russian], Workshop DHA & CAGD. Selected Topics. 18 September 2007. ( http://dha.spb.ru/reps07.shtml#0918 ).
18. V. N. Malozemov and A. B. Pevnyi, "The fourth definition of a tight frame" [in Russian], Workshop DHA & CAGD. Selected Topics. 30 May 2007. ( http://dha.spb.ru/reps07.shtml#0530 ).
19. V. N. Malozemov and N. A. Solov'eva, "On unitary matrices and singular decompositions" [in Russian], Workshop DHA & CAGD. Selected Topics. 30 January 2008. ( http://dha.spb.ru/reps08.shtml#0130 ).
20. V. N. Malozemov and A. B. Pevnyi, "There are no Mercedes-Benz Systems for m∈>∈n ∈+∈1" [in Russian], Workshop DHA & CAGD. Selected Topics. 13 February 2008. ( http://dha.spb.ru/reps08. shtml#0213 ).
21. A. B. Pevnyi, "Frames in finite-dimensional spaces and minimization of the frame potential" [in Russian], Workshop DHA & CAGD. Selected Topics. 28 March 2006. ( http://dha.spb.ru/reps06.shtml#0328 )
22. A. N. Sabaev, "Note on Mercedes-Benz systems" [in Russian], Workshop DHA & CAGD. Selected Topics. 16 September 2008. ( http://dha.spb.ru/reps08.shtml#0916 )
23. M. N. Istomina and A. B. Pevnyi, "The Mercedes-Benz frame in the n-dimensional space" [in Russian], Vestnik Syktyvkar. Gos. Univ. Ser. 1 No. 6, 219-222 (2006).
24. M. N. Istomina and A. B. Pevnyi, "On location of points on a sphere and the Mercedes-Benz frame" [in Russian], Mat. Prosveschenie. Ser. 3 No. 11, 105-112 (2007).
25. V. N. Malozemov and A. B. Pevnyi, "Mercedes-Benz systems and tight frames" [in Russian], Vestnik Syktyvkar. Gos. Univ. Ser. 1 No. 7, 141-154 (2007).
26. N. N. Andreev and V. A. Yudin, "Extremal location of points on a sphere" [in Russian], Mat. Prosveschenie. Ser. 3 No. 1, 115-121 (1997).
27. B Reznick 1992 Sums of even powers of real linear forms Mem. Am. Math. Soc. 96 463 1 155
28. J. J. Benedetto and J. D. Kolesar, "Geometric properties of Grassmannian frames for ℝ2 and ℝ3," EURASIP J. Appl. Signal Process. (2006), ID 49850, 1-17.
29. MA Sustik JA Tropp IS Dhillon RW Heath 2007 On the existence of equiangular tight frames Linear Algebra Appl. 426 619 635
30. JA Tropp IS Dhillon RW Heath T Strohmer 2005 Designing structured tight frames via an alternating projection method IEEE Trans. Inf. Theory 51 188 209
31. D Han DR Larson 2000 Frames, bases and group representation Mem. Am. Math. Soc. 147 697 1 94
32. R Vale S Waldron 2005 Tight frames and their symmetries Const. Approx. 21 1 83 112
33. B. Venkov, "Réseaux et designs sphériques," In: Réseaux Euclidiens, Designs sphériques et Formes Modulaires, Enseign. Math., Gèneve (2001), pp. 10-86.
34. S Waldron 2003 Generalised Welch bound equality sequences are tight frames IEEE Trans. Inf. Theory 49 9 2307 2009
35. S. Waldron and N. Hay, "On computing all harmonic frames of n vectors in double struck M sign Cd ," Appl. Comput. Harmonic Anal. 21, 168-181 (2006)
36. P Xia S Zhou GB Giannakis 2005 Achieving the Welch bound with difference sets IEEE Trans. Inf. Theory 51 5 1900 1907
37. V. V. Voevodin and Vl. V. Voevodin, Handbook on Linear Algebra. Electronic System LINEAL [in Russian], St.-Petersburg (2006).