메뉴 건너뛰기




Volumn 55, Issue 12, 2009, Pages 5742-5757

Uncertainty relations for shift-invariant analog signals

Author keywords

Analog compressed sensing; Coherence; Shift invariant signals; Sparse decompositions; Uncertainty relations.

Indexed keywords

COHERENCE; COMPRESSED SENSING; SHIFT INVARIANT; SPARSE DECOMPOSITION; UNCERTAINTY RELATION;

EID: 77949747117     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2032711     Document Type: Article
Times cited : (30)

References (33)
  • 1
    • 84939751170 scopus 로고
    • Prolate spheroidal wave functions, Fourier analysis and uncertainty-I
    • D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-I," Bell Syst. Tech. J, vol.40, pp. 43-64, 1961.
    • (1961) Bell Syst. Tech. J , vol.40 , pp. 43-64
    • Slepian, D.1    Pollak, H.O.2
  • 2
    • 84857887285 scopus 로고
    • Prolate spheroidal wave functions, Fourier analysis and uncertainty-II
    • H. J. Landau and H. O. Pollack, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-II," Bell Syst. Tech. J, vol.40, pp. 65-84, 1961.
    • (1961) Bell Syst. Tech. J , vol.40 , pp. 65-84
    • Landau, H.J.1    Pollack, H.O.2
  • 3
    • 84944487979 scopus 로고
    • Prolate spheroidal wave functions, Fourier analysis and uncertainty-III
    • H. J. Landau and H. O. Pollack, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-III," Bell Syst. Tech. J, vol.41, pp. 1295-1336, 1962.
    • (1962) Bell Syst. Tech. J , vol.41 , pp. 1295-1336
    • Landau, H.J.1    Pollack, H.O.2
  • 4
    • 0001616908 scopus 로고
    • Uncertainty principles and signal recovery
    • D. L. Donoho and P. B. Stark, "Uncertainty principles and signal recovery," SIAM J. Appl. Math., vol.49, no.3, pp. 906-931, 1989.
    • (1989) SIAM J. Appl. Math. , vol.49 , Issue.3 , pp. 906-931
    • Donoho, D.L.1    Stark, P.B.2
  • 5
    • 0000293183 scopus 로고
    • Theory of communications
    • D. Gabor, "Theory of communications," J. Inst. Elec. Eng., vol.93, pp. 429-457, 1946.
    • (1946) J. Inst. Elec. Eng. , vol.93 , pp. 429-457
    • Gabor, D.1
  • 6
    • 0035504028 scopus 로고    scopus 로고
    • Uncertainty principles and ideal atomic decomposition
    • Nov.
    • D. L. Donoho and X. Huo, "Uncertainty principles and ideal atomic decomposition," IEEE Trans. Inf. Theory, vol.47, no.7, pp. 2845-2862, Nov. 2001.
    • (2001) IEEE Trans. Inf. Theory , vol.47 , Issue.7 , pp. 2845-2862
    • Donoho, D.L.1    Huo, X.2
  • 7
    • 0036714214 scopus 로고    scopus 로고
    • A generalized uncertainty principle and sparse representation in pairs of bases
    • Sep.
    • M. Elad and A. M. Bruckstein, "A generalized uncertainty principle and sparse representation in pairs of bases," IEEE Trans. Inf. Theory, vol.48, no.9, pp. 2558-2567, Sep. 2002.
    • (2002) IEEE Trans. Inf. Theory , vol.48 , Issue.9 , pp. 2558-2567
    • Elad, M.1    Bruckstein, A.M.2
  • 8
    • 33744726904 scopus 로고    scopus 로고
    • Quantitative robust uncertainty principles and optimally sparse decompositions
    • E. J. Candes and J. Romberg, "Quantitative robust uncertainty principles and optimally sparse decompositions," Foundations of Comput. Math., vol.6, no.2, pp. 227-254, 2006.
    • (2006) Foundations of Comput. Math. , vol.6 , Issue.2 , pp. 227-254
    • Candes, E.J.1    Romberg, J.2
  • 9
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Apr.
    • D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol.52, no.4, pp. 1289-1306, Apr. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.L.1
  • 10
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • Feb.
    • E. J. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol.52, no.2, pp. 489-509, Feb. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.2 , pp. 489-509
    • Candès, E.J.1    Romberg, J.2    Tao, T.3
  • 11
    • 0038718564 scopus 로고    scopus 로고
    • On sparse representation in pairs of bases
    • Jun.
    • A. Feuer and A. Nemirovski, "On sparse representation in pairs of bases," IEEE Trans. Inf. Theory, vol.49, no.6, pp. 1579-1581, Jun. 2003.
    • (2003) IEEE Trans. Inf. Theory , vol.49 , Issue.6 , pp. 1579-1581
    • Feuer, A.1    Nemirovski, A.2
  • 12
    • 0347968052 scopus 로고    scopus 로고
    • Sparse representations in unions of bases
    • Dec.
    • R. Gribonval and M. Nielsen, "Sparse representations in unions of bases," IEEE Trans. Inf. Theory, vol.49, no.12, pp. 3320-3325, Dec. 2003.
    • (2003) IEEE Trans. Inf. Theory , vol.49 , Issue.12 , pp. 3320-3325
    • Gribonval, R.1    Nielsen, M.2
  • 13
    • 0037418225 scopus 로고    scopus 로고
    • Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization
    • D. L. Donoho and M. Elad, "Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization," Proc. Nat. Acad. Sci., vol.100, no.5, pp. 2197-2202, 2003.
    • (2003) Proc. Nat. Acad. Sci. , vol.100 , Issue.5 , pp. 2197-2202
    • Donoho, D.L.1    Elad, M.2
  • 14
    • 5444237123 scopus 로고    scopus 로고
    • Greed is good: Algorithmic results for sparse approximation
    • Oct.
    • J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol.50, no.10, pp. 2231-2242, Oct. 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.50 , Issue.10 , pp. 2231-2242
    • Tropp, J.A.1
  • 15
    • 0027842081 scopus 로고
    • Matching pursuits with time-frequency dictionaries
    • Dec.
    • S. G. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process., vol.41, no.12, pp. 3397-3415, Dec. 1993.
    • (1993) IEEE Trans. Signal Process. , vol.41 , Issue.12 , pp. 3397-3415
    • Mallat, S.G.1    Zhang, Z.2
  • 16
    • 43949161106 scopus 로고
    • 2 ℝ
    • C. de Boor, R. DeVore, and A. Ron, "The structure of finitely generated shift-invariant spaces in L 2 ℝ," J. Funct. Anal., vol.119, no.1, pp. 37-78, 1994.
    • (1994) J. Funct. Anal. , vol.119 , Issue.1 , pp. 37-78
    • De Boor, C.1    Devore, R.2    Ron, A.3
  • 17
    • 0001544864 scopus 로고
    • Fractal functions and wavelet expansions based on several scaling functions
    • J. S. Geronimo, D. P. Hardin, and P. R. Massopust, "Fractal functions and wavelet expansions based on several scaling functions," J. Approx. Theory, vol.78, no.3, pp. 373-401, 1994.
    • (1994) J. Approx. Theory , vol.78 , Issue.3 , pp. 373-401
    • Geronimo, J.S.1    Hardin, D.P.2    Massopust, P.R.3
  • 18
    • 23944435876 scopus 로고    scopus 로고
    • Generalized shift-invariant systems and frames for subspaces
    • O. Christensen and Y. C. Eldar, "Generalized shift-invariant systems and frames for subspaces," J. Fourier Analys. Appl., vol.11, pp. 299-313, 2005.
    • (2005) J. Fourier Analys. Appl. , vol.11 , pp. 299-313
    • Christensen, O.1    Eldar, Y.C.2
  • 20
    • 61549103040 scopus 로고    scopus 로고
    • Blind multiband signal reconstruction: Compressed sensing for analog signals
    • Mar.
    • M. Mishali and Y. C. Eldar, "Blind multiband signal reconstruction: Compressed sensing for analog signals," IEEE Trans. Signal Process., vol.57, no.3, pp. 993-1009, Mar. 2009.
    • (2009) IEEE Trans. Signal Process. , vol.57 , Issue.3 , pp. 993-1009
    • Mishali, M.1    Eldar, Y.C.2
  • 21
    • 53149111169 scopus 로고    scopus 로고
    • Reduce and boost: Recovering arbitrary sets of jointly sparse vectors
    • Oct.
    • M. Mishali and Y. C. Eldar, "Reduce and boost: Recovering arbitrary sets of jointly sparse vectors," IEEE Trans. Signal Process., vol.56, no.10, pp. 4692-4702, Oct. 2008.
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.10 , pp. 4692-4702
    • Mishali, M.1    Eldar, Y.C.2
  • 22
    • 68249162101 scopus 로고    scopus 로고
    • Compressed sensing of analog signals in shift-invariant spaces
    • Aug.
    • Y. C. Eldar, "Compressed sensing of analog signals in shift-invariant spaces," IEEE Trans. Signal Process., vol.57, no.8, pp. 2986-2997, Aug. 2009.
    • (2009) IEEE Trans. Signal Process. , vol.57 , Issue.8 , pp. 2986-2997
    • Eldar, Y.C.1
  • 23
    • 84946596811 scopus 로고    scopus 로고
    • From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals
    • [Online]. Available: arXiv 0902.4291, to be published
    • M. Mishali and Y. C. Eldar, "From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals," IEEE Sel. Topics Signal Process. [Online]. Available: arXiv 0902.4291, to be published
    • IEEE Sel. Topics Signal Process
    • Mishali, M.1    Eldar, Y.C.2
  • 24
    • 70350743173 scopus 로고    scopus 로고
    • Robust recovery of signals from a structured union of subspaces
    • Nov.
    • Y. C. Eldar and M. Mishali, "Robust recovery of signals from a structured union of subspaces," IEEE Trans. Inf. Theory, vol.55, no.11, pp. 5302-5316, Nov. 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.11 , pp. 5302-5316
    • Eldar, Y.C.1    Mishali, M.2
  • 25
    • 33947142837 scopus 로고    scopus 로고
    • Theoretical results on sparse representations of multiple-measurement vectors
    • Dec.
    • J. Chen and X. Huo, "Theoretical results on sparse representations of multiple-measurement vectors," IEEE Trans. Signal Process., vol.54, no.12, pp. 4634-4643, Dec. 2006.
    • (2006) IEEE Trans. Signal Process. , vol.54 , Issue.12 , pp. 4634-4643
    • Chen, J.1    Huo, X.2
  • 26
    • 23844477225 scopus 로고    scopus 로고
    • Sparse solutions to linear inverse problems with multiple measurement vectors
    • Jul.
    • S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, "Sparse solutions to linear inverse problems with multiple measurement vectors," IEEE Trans. Signal Process., vol.53, no.7, pp. 2477-2488, Jul. 2005.
    • (2005) IEEE Trans. Signal Process. , vol.53 , Issue.7 , pp. 2477-2488
    • Cotter, S.F.1    Rao, B.D.2    Engan, K.3    Kreutz-Delgado, K.4
  • 27
    • 85032751311 scopus 로고    scopus 로고
    • Beyond bandlimited sampling
    • May
    • Y. C. Eldar and T. Michaeli, "Beyond bandlimited sampling," IEEE Signal Process. Mag., vol.26, no.3, pp. 48-68, May 2009.
    • (2009) IEEE Signal Process. Mag. , vol.26 , Issue.3 , pp. 48-68
    • Eldar, Y.C.1    Michaeli, T.2
  • 28
    • 70350716339 scopus 로고    scopus 로고
    • Low rate sampling schemes for time delay estimation
    • submitted for publication
    • K. Gedalyahu and Y. C. Eldar, "Low rate sampling schemes for time delay estimation," IEEE Trans. Signal Process., submitted for publication.
    • IEEE Trans. Signal Process
    • Gedalyahu, K.1    Eldar, Y.C.2
  • 30
    • 48749101457 scopus 로고
    • Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
    • J. B. Kruskal, "Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics," Linear Alg. Its Applic., vol.18, no.2, pp. 95-138, 1977.
    • (1977) Linear Alg. Its Applic. , vol.18 , Issue.2 , pp. 95-138
    • Kruskal, J.B.1
  • 31
    • 73849109362 scopus 로고    scopus 로고
    • Average case analysis of multichannel sparse recovery using convex relaxation
    • to be published
    • Y. C. Eldar and H. Rauhut, "Average case analysis of multichannel sparse recovery using convex relaxation," IEEE Trans. Inf. Theory, to be published.
    • IEEE Trans. Inf. Theory
    • Eldar, Y.C.1    Rauhut, H.2
  • 33
    • 46749136514 scopus 로고    scopus 로고
    • Nonuniform sampling of periodic bandlimited signals
    • Jul.
    • E. Margolis and Y. C. Eldar, "Nonuniform sampling of periodic bandlimited signals," IEEE Trans. Signal Process., vol.56, no.7, pp. 2728-2745, Jul. 2008.
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.7 , pp. 2728-2745
    • Margolis, E.1    Eldar, Y.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.