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Volumn 55, Issue 4, 2009, Pages 1872-1882

Sampling theorems for signals from the union of finite-dimensional linear subspaces

Author keywords

Compressed sensing; Embedding and restricted isometry; Sampling theorems; Unions of linear subspaces

Indexed keywords

COMPRESSED SENSING; CONVEX HULLS; EMBEDDING AND RESTRICTED ISOMETRY; LINEAR ALGORITHMS; LINEAR MAPS; LINEAR SAMPLINGS; LIPSCHITZ CONSTANTS; MODEL PARAMETERS; NUMBER OF SAMPLES; NYQUIST; NYQUIST RATES; OBSERVATION SPACES; ORTHONORMAL BASIS; SAMPLING METHODS; SAMPLING STRATEGIES; SAMPLING THEOREMS; SHANNON SAMPLING THEOREMS; SIGNAL ACQUISITIONS; SIGNAL MODELS; SPARSE REPRESENTATIONS; SPARSE SIGNAL MODELS; SUFFICIENT CONDITIONS; TREE STRUCTURES; UNIONS OF LINEAR SUBSPACES;

EID: 64549135334     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2013003     Document Type: Article
Times cited : (232)

References (35)
  • 1
    • 79957590676 scopus 로고
    • Certain topics in telegraph transmission theory
    • Feb
    • H. Nyquist, "Certain topics in telegraph transmission theory," Trans. Amer. Inst. Electr. Eng., pp. 617-644, Feb. 1928.
    • (1928) Trans. Amer. Inst. Electr. Eng , pp. 617-644
    • Nyquist, H.1
  • 3
    • 0031102203 scopus 로고    scopus 로고
    • Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm
    • Mar
    • I. F. Gorodnitsky and B. D. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Trans. Signal Process., vol. 45, no. 3, pp. 600-616, Mar. 1997.
    • (1997) IEEE Trans. Signal Process , vol.45 , Issue.3 , pp. 600-616
    • Gorodnitsky, I.F.1    Rao, B.D.2
  • 4
    • 0036612082 scopus 로고    scopus 로고
    • Sampling signals with finite rate of innovation
    • Jun
    • M. Vetterli, P. Marziliano, and T. Blu, "Sampling signals with finite rate of innovation," IEEE Trans. Signal Process., vol. 50, no. 6, pp. 1417-1428, Jun. 2002.
    • (2002) IEEE Trans. Signal Process , vol.50 , Issue.6 , pp. 1417-1428
    • Vetterli, M.1    Marziliano, P.2    Blu, T.3
  • 5
    • 84864322995 scopus 로고    scopus 로고
    • arXiv:0806. 3332v1
    • Y. C. Eldar, "Compressed sensing of analog signals," arXiv:0806. 3332v1, 2008.
    • (2008)
    • Eldar, Y.C.1
  • 6
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • Feb
    • E. 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.1    Romberg, J.2    Tao, T.3
  • 7
    • 33744726904 scopus 로고    scopus 로고
    • Quantitative robust uncertainty principles and optimally sparse decompositions
    • E. Candès and J. Romberg, "Quantitative robust uncertainty principles and optimally sparse decompositions," Found. Comput. Math vol. 6, no. 2, pp. 227-254, 2006.
    • (2006) Found. Comput. Math , vol.6 , Issue.2 , pp. 227-254
    • Candès, E.1    Romberg, J.2
  • 8
    • 33947416035 scopus 로고    scopus 로고
    • Near optimal signal recovery from random projections: Universal encoding strategies?
    • Dec
    • E. Candès and T. Tao, "Near optimal signal recovery from random projections: Universal encoding strategies?," IEEE Trans. Inf. Theory, vol. 52, no. 12, pp. 5406-5425, Dec. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candès, E.1    Tao, T.2
  • 9
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Apr
    • D. 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.1
  • 10
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math. vol. 59, no. 8, pp. 1207-1223, 2006.
    • (2006) Commun. Pure Appl. Math , vol.59 , Issue.8 , pp. 1207-1223
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 11
    • 57349181932 scopus 로고    scopus 로고
    • Compressed sensing and best k-term approximation
    • A. Cohen, W. Dahmen, and R. DeVore, "Compressed sensing and best k-term approximation," J. Amer. Math. Soc., vol. 22, no. 1, pp. 211-231, 2009.
    • (2009) J. Amer. Math. Soc , vol.22 , Issue.1 , pp. 211-231
    • Cohen, A.1    Dahmen, W.2    DeVore, R.3
  • 12
    • 43749118418 scopus 로고    scopus 로고
    • Compressed sensing and redundant dictionaries
    • May
    • H. Rauhut, K. Schnass, and P. Vandergheynst, "Compressed sensing and redundant dictionaries," IEEE Trans. Inf. Theory, vol. 54, no. 5, pp. 2210-2219, May 2007.
    • (2007) IEEE Trans. Inf. Theory , vol.54 , Issue.5 , pp. 2210-2219
    • Rauhut, H.1    Schnass, K.2    Vandergheynst, P.3
  • 13
    • 38149032997 scopus 로고    scopus 로고
    • Compressed sensing and source separation
    • Independent Component Analysis and Blind Source Separation, M. E. Davies, C. J. James, S. Abdallah, and M. D. Plumbley, Eds. New York: Springer-Verlag
    • T. Blumensath and M. Davies, "Compressed sensing and source separation," in Independent Component Analysis and Blind Source Separation, ser. Lecture Notes on Computer Science 4666, M. E. Davies, C. J. James, S. Abdallah, and M. D. Plumbley, Eds. New York: Springer-Verlag, 2007, pp. 341-348.
    • (2007) ser. Lecture Notes on Computer Science , vol.4666 , pp. 341-348
    • Blumensath, T.1    Davies, M.2
  • 15
    • 33748575920 scopus 로고    scopus 로고
    • Signal reconstruction from noisy random projections
    • Sep
    • J. Haupt and R. Nowak, "Signal reconstruction from noisy random projections," IEEE Trans. Inf. Theory, vol. 52, no. 9, pp. 4036-4048, Sep. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.9 , pp. 4036-4048
    • Haupt, J.1    Nowak, R.2
  • 16
    • 34548275795 scopus 로고    scopus 로고
    • The dantzig selector: Statistical estimation when p is larger than n
    • E. Candès and T. Tao, "The dantzig selector: Statistical estimation when p is larger than n," Ann. Statist., vol. 35, no. 6, pp. 2313-2351, 2007.
    • (2007) Ann. Statist , vol.35 , Issue.6 , pp. 2313-2351
    • Candès, E.1    Tao, T.2
  • 17
    • 44849115269 scopus 로고    scopus 로고
    • A theory for sampling signals from a union of subspaces
    • Jun
    • Y. Lu and M. Do, "A theory for sampling signals from a union of subspaces," IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2334-2345, Jun. 2008.
    • (2008) IEEE Trans. Signal Process , vol.56 , Issue.6 , pp. 2334-2345
    • Lu, Y.1    Do, M.2
  • 18
    • 30844432177 scopus 로고    scopus 로고
    • C. La and M. Do, Signal reconstruction using sparse tree representations, in Proc. SPIE Conf. Wavelet Appl. Signal Image Process. XI, San Diego, CA, Sep. 2005, 5914.
    • C. La and M. Do, "Signal reconstruction using sparse tree representations," in Proc. SPIE Conf. Wavelet Appl. Signal Image Process. XI, San Diego, CA, Sep. 2005, vol. 5914.
  • 19
    • 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. K-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    K-Delgado, K.4
  • 20
    • 33947142837 scopus 로고    scopus 로고
    • Theoretical results on sparse representations of multiple-measurement vectors
    • Dec
    • C. J. 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
  • 21
    • 30844445842 scopus 로고    scopus 로고
    • Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit
    • J. A. Tropp, A. C. Gilbert, and M. J. Strauss, "Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit," Signal Process., vol. 86, pp. 572-588, 2006.
    • (2006) Signal Process , vol.86 , pp. 572-588
    • Tropp, J.A.1    Gilbert, A.C.2    Strauss, M.J.3
  • 22
    • 30844461481 scopus 로고    scopus 로고
    • Algorithms for simultaneous sparse approximation. Part II: Convex relaxation
    • J. A. Tropp, "Algorithms for simultaneous sparse approximation. Part II: Convex relaxation," Signal Process., vol. 86, pp. 589-602, 2006.
    • (2006) Signal Process , vol.86 , pp. 589-602
    • Tropp, J.A.1
  • 23
    • 57349143370 scopus 로고    scopus 로고
    • Atoms of all channels, unite! average case analysis of multi-channel sparse recovery using greedy algorithms
    • Oct, DOI:10.1007/s00041-008-9044-y
    • K. S. R. Gribonval, H. Rauhut, and P. Vandergheynst, "Atoms of all channels, unite! average case analysis of multi-channel sparse recovery using greedy algorithms," J. Fourier Anal. Appl., Oct. 2008, DOI:10.1007/s00041-008-9044-y.
    • (2008) J. Fourier Anal. Appl
    • Gribonval, K.S.R.1    Rauhut, H.2    Vandergheynst, P.3
  • 26
    • 33751278790 scopus 로고    scopus 로고
    • T. Sauer, J. A. Yorke, and M. Casdagli, Embedology, J. Statist. Phys., 65, no. 3/4, pp. 579-616, 1991.
    • T. Sauer, J. A. Yorke, and M. Casdagli, "Embedology," J. Statist. Phys., vol. 65, no. 3/4, pp. 579-616, 1991.
  • 27
    • 84967728280 scopus 로고
    • Prevalence: A translation-invariant "almost every" on infinite-dimensional spaces
    • R. Hunt, T. Sauer, and A. Yorke, "Prevalence: A translation-invariant "almost every" on infinite-dimensional spaces," Bull. Amer. Math. Soc., vol. 99, no. 11, pp. 217-238, 1992.
    • (1992) Bull. Amer. Math. Soc , vol.99 , Issue.11 , pp. 217-238
    • Hunt, R.1    Sauer, T.2    Yorke, A.3
  • 28
    • 58849146227 scopus 로고    scopus 로고
    • Random projections of smooth manifolds
    • Sep, DOI:10.1007/s10208-007-9011-z
    • R. Baraniuk and M. Wakin, "Random projections of smooth manifolds," Found. Comput. Math., Sep. 2007, DOI:10.1007/s10208-007-9011-z.
    • (2007) Found. Comput. Math
    • Baraniuk, R.1    Wakin, M.2
  • 29
    • 0037418225 scopus 로고    scopus 로고
    • Optimally-sparse representation in general (non-orthogonal) dictionaries via l1 minimization
    • D. L. Donoho and M. Elad, "Optimally-sparse representation in general (non-orthogonal) dictionaries via l1 minimization," in Proc. Nat. Acad. Sci., 2003, vol. 100, pp. 2197-2202.
    • (2003) Proc. Nat. Acad. Sci , vol.100 , pp. 2197-2202
    • Donoho, D.L.1    Elad, M.2
  • 30
    • 33646365077 scopus 로고    scopus 로고
    • For most large underdetermined systems of linear equations the minimal 1-norm solution is also the sparsest solution
    • D. L. Donoho, "For most large underdetermined systems of linear equations the minimal 1-norm solution is also the sparsest solution," Commun. Pure Appl. Math., vol. 59, no. 6, pp. 797-829, 2006.
    • (2006) Commun. Pure Appl. Math , vol.59 , Issue.6 , pp. 797-829
    • Donoho, D.L.1
  • 31
    • 34548266934 scopus 로고    scopus 로고
    • The geometry of low-dimensional signal manifolds,
    • Ph.D. dissertation, Electr. Comput. Eng, Rice Univ, Houston, TX
    • M. B. Wakin, "The geometry of low-dimensional signal manifolds," Ph.D. dissertation, Electr. Comput. Eng., Rice Univ., Houston, TX, 2006.
    • (2006)
    • Wakin, M.B.1
  • 33
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • Dec
    • E. J. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candès, E.J.1    Tao, T.2
  • 34
    • 55649115527 scopus 로고    scopus 로고
    • A simple proof of the restricted isometry property for random matrices
    • Feb, DOI:10.1007/s00365-007-9003-x
    • R. Baraniuk, M. Davenport, R. De Vore, and M. Wakin, "A simple proof of the restricted isometry property for random matrices," Constructive Approx., Feb. 2008, DOI:10.1007/s00365-007-9003-x.
    • (2008) Constructive Approx
    • Baraniuk, R.1    Davenport, M.2    De Vore, R.3    Wakin, M.4
  • 35
    • 84878104490 scopus 로고    scopus 로고
    • Compressive sampling
    • Madrid, Spain
    • E. Candés, "Compressive sampling," in Proc. Int. Congr. Math. Madrid, Spain, 2006, vol. 3, pp. 1433-1452.
    • (2006) Proc. Int. Congr. Math , vol.3 , pp. 1433-1452
    • Candés, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.