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Volumn 55, Issue 10, 2009, Pages 4723-4741

Comparing measures of sparsity

Author keywords

Measures of sparsity; Measuring sparsity; Sparse distribution; Sparse representation; Sparsity

Indexed keywords

MEASURES OF SPARSITY; MEASURING SPARSITY; SPARSE DISTRIBUTION; SPARSE REPRESENTATION; SPARSITY;

EID: 70349622761     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2027527     Document Type: Article
Times cited : (722)

References (51)
  • 1
    • 40749116889 scopus 로고    scopus 로고
    • Estimation of rapidly time-varying sparse channels
    • Oct
    • W. Li and J. Preisig, "Estimation of rapidly time-varying sparse channels," IEEE J. Ocean. Eng., vol. 32, no. 4, pp. 927-939, Oct. 2007.
    • (2007) IEEE J. Ocean. Eng , vol.32 , Issue.4 , pp. 927-939
    • Li, W.1    Preisig, J.2
  • 2
    • 40549122347 scopus 로고    scopus 로고
    • Sparse pseudo inverse of the discrete plane wave transform
    • Feb
    • R. Adams, Y. Xu, and F. Canning, "Sparse pseudo inverse of the discrete plane wave transform," IEEE Trans. Antennas Propag., vol. 56, no. 2, pp. 475-484, Feb. 2008.
    • (2008) IEEE Trans. Antennas Propag , vol.56 , Issue.2 , pp. 475-484
    • Adams, R.1    Xu, Y.2    Canning, F.3
  • 4
    • 39149089704 scopus 로고    scopus 로고
    • Sparse representation for color image restoration
    • Jan
    • J. Mairal, M. Elad, and G. Sapiro, "Sparse representation for color image restoration," IEEE Trans. Image Processing, vol. 17, no. 1, pp. 53-69, Jan. 2008.
    • (2008) IEEE Trans. Image Processing , vol.17 , Issue.1 , pp. 53-69
    • Mairal, J.1    Elad, M.2    Sapiro, G.3
  • 5
    • 67349251766 scopus 로고    scopus 로고
    • Sparse and redundant modeling of image content using an image-signature-dictionary
    • M. Aharon and M. Elad, "Sparse and redundant modeling of image content using an image-signature-dictionary," SIAM J. Imag. Sci., vol. 1, no. 3, pp. 228-247, 2008.
    • (2008) SIAM J. Imag. Sci , vol.1 , Issue.3 , pp. 228-247
    • Aharon, M.1    Elad, M.2
  • 7
    • 0031140712 scopus 로고    scopus 로고
    • Highly scalable parallel algorithms for sparse matrix factorization
    • May
    • A. Gupta, G. Karypis, and V. Kumar, "Highly scalable parallel algorithms for sparse matrix factorization," IEEE Trans. Parallel Distrib. Syst., vol. 8, no. 5, pp. 502-520, May 1997.
    • (1997) IEEE Trans. Parallel Distrib. Syst , vol.8 , Issue.5 , pp. 502-520
    • Gupta, A.1    Karypis, G.2    Kumar, V.3
  • 8
    • 33645712308 scopus 로고    scopus 로고
    • Just relax: Convex programming methods for identifying sparse signals in noise
    • Mar
    • J. Tropp, "Just relax: Convex programming methods for identifying sparse signals in noise," IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 1030-1051, Mar. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.3 , pp. 1030-1051
    • Tropp, J.1
  • 10
    • 46749116519 scopus 로고    scopus 로고
    • Stable recovery of sparse signals via regularized minimization
    • Jul
    • C. Zhu, "Stable recovery of sparse signals via regularized minimization," IEEE Trans. Inf. Theory, vol. 54, no. 7, pp. 3364-3367, Jul. 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , Issue.7 , pp. 3364-3367
    • Zhu, C.1
  • 11
    • 53149111169 scopus 로고    scopus 로고
    • Reduce and boost: Recovering arbitrary sets of jointly sparse vectors
    • Oct
    • M. Mishali and Y. Eldar, "Reduce and boost: Recovering arbitrary sets of jointly sparse vectors," IEEE Trans. Signal Processing, vol. 56, no. 10, pp. 4692-4702, Oct. 2008.
    • (2008) IEEE Trans. Signal Processing , vol.56 , Issue.10 , pp. 4692-4702
    • Mishali, M.1    Eldar, Y.2
  • 12
    • 33750383209 scopus 로고    scopus 로고
    • K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation
    • Nov
    • M. Aharon, M. Elad, and A. Bruckstein, "K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation," IEEE Trans. Signal Processing, vol. 54, no. 11, pp. 4311-4322, Nov. 2006.
    • (2006) IEEE Trans. Signal Processing , vol.54 , Issue.11 , pp. 4311-4322
    • Aharon, M.1    Elad, M.2    Bruckstein, A.3
  • 13
    • 44849094084 scopus 로고    scopus 로고
    • A frame construction and a universal distortion bound for sparse representations
    • Jun
    • M. Akcakaya and V. Tarokh, "A frame construction and a universal distortion bound for sparse representations," IEEE Trans. Signal Processing, vol. 56, no. 6, pp. 2443-2450, Jun. 2008.
    • (2008) IEEE Trans. Signal Processing , vol.56 , Issue.6 , pp. 2443-2450
    • Akcakaya, M.1    Tarokh, V.2
  • 14
    • 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
  • 15
    • 33751004125 scopus 로고    scopus 로고
    • Multi-frame representations in linear inverse problems with mixed multi-constraints
    • G. Teschke, "Multi-frame representations in linear inverse problems with mixed multi-constraints," Appl. Computat. Harmon. Anal., vol. 22, no. 1, pp. 43-60, 2007.
    • (2007) Appl. Computat. Harmon. Anal , vol.22 , Issue.1 , pp. 43-60
    • Teschke, G.1
  • 16
    • 34248636293 scopus 로고    scopus 로고
    • Fast sparse approximation for least squares support vector machine
    • May
    • L. Jiao, L. Bo, and L. Wang, "Fast sparse approximation for least squares support vector machine," IEEE Trans. Neural Netw., vol. 18, no. 3, pp. 685-697, May 2007.
    • (2007) IEEE Trans. Neural Netw , vol.18 , Issue.3 , pp. 685-697
    • Jiao, L.1    Bo, L.2    Wang, L.3
  • 18
    • 85032750944 scopus 로고    scopus 로고
    • Compressive sampling and lossy compression
    • Mar
    • V. Goyal, A. Fletcher, and S. Rangan, "Compressive sampling and lossy compression," IEEE Signal Processing Mag., vol. 25, no. 2, pp. 48-56, Mar. 2008.
    • (2008) IEEE Signal Processing Mag , vol.25 , Issue.2 , pp. 48-56
    • Goyal, V.1    Fletcher, A.2    Rangan, S.3
  • 19
    • 70349612743 scopus 로고    scopus 로고
    • The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem
    • M. Fornasier, R. Ramlau, and G. Teschke, "The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem," Adv. Computat. Math., 2008.
    • (2008) Adv. Computat. Math
    • Fornasier, M.1    Ramlau, R.2    Teschke, G.3
  • 20
    • 25444508285 scopus 로고    scopus 로고
    • P. O'Grady, B. Pearlmutter, and S. Rickard, Survey of sparse and non-sparse methods in source separation, Int. J. Imag. Syst. Technol., 15, Special Issue on Blind Source Separation and Deconvolution in Imaging and Image Processing, no. 1, pp. 18-33, Jul. 2005.
    • P. O'Grady, B. Pearlmutter, and S. Rickard, "Survey of sparse and non-sparse methods in source separation," Int. J. Imag. Syst. Technol., vol. 15, Special Issue on Blind Source Separation and Deconvolution in Imaging and Image Processing, no. 1, pp. 18-33, Jul. 2005.
  • 21
    • 41549086470 scopus 로고    scopus 로고
    • Convolutive blind source separation in the frequency domain based on sparse representation
    • Jul
    • Z. He, S. Xie, S. Ding, and A. Cichocki, "Convolutive blind source separation in the frequency domain based on sparse representation," IEEE Trans. Audio, Speech, Language Processing, vol. 15, no. 5, pp. 1551-1563, Jul. 2007.
    • (2007) IEEE Trans. Audio, Speech, Language Processing , vol.15 , Issue.5 , pp. 1551-1563
    • He, Z.1    Xie, S.2    Ding, S.3    Cichocki, A.4
  • 22
    • 85132940694 scopus 로고    scopus 로고
    • The DUET blind source separation algorithm
    • New York: Springer-Verlag
    • S. Rickard, "The DUET blind source separation algorithm," in Blind Speech Separation. New York: Springer-Verlag, 2007, pp. 217-241.
    • (2007) Blind Speech Separation , pp. 217-241
    • Rickard, S.1
  • 23
    • 3142694930 scopus 로고    scopus 로고
    • Blind separation of speech mixtures via time-frequency masking
    • Jul
    • O. Yilmaz and S. Rickard, "Blind separation of speech mixtures via time-frequency masking," IEEE Trans. Signal Processing, vol. 52, no. 7, pp. 1830-1847, Jul. 2004.
    • (2004) IEEE Trans. Signal Processing , vol.52 , Issue.7 , pp. 1830-1847
    • Yilmaz, O.1    Rickard, S.2
  • 24
    • 33645744108 scopus 로고    scopus 로고
    • Sparse representations are most likely to be the sparsest possible
    • M. Elad, "Sparse representations are most likely to be the sparsest possible," in EURASIP J. Appl. Signal Processing, 2006.
    • (2006) EURASIP J. Appl. Signal Processing
    • Elad, M.1
  • 25
    • 55349132734 scopus 로고    scopus 로고
    • On the uniqueness of non-negative sparse solutions to underdetermined systems of equations
    • Nov
    • A. Bruckstein, M. Elad, and M. Zibulevsky, "On the uniqueness of non-negative sparse solutions to underdetermined systems of equations," IEEE Trans. Inf. Theory, vol. 54, no. 11, pp. 4813-4820, Nov. 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , Issue.11 , pp. 4813-4820
    • Bruckstein, A.1    Elad, M.2    Zibulevsky, M.3
  • 27
    • 0000299688 scopus 로고
    • The measurement of the inequity of incomes
    • H. Dalton, "The measurement of the inequity of incomes," Econom. J. vol. 30, pp. 348-361, 1920.
    • (1920) Econom. J , vol.30 , pp. 348-361
    • Dalton, H.1
  • 30
    • 4544294317 scopus 로고    scopus 로고
    • Measuring sparseness of noisy signals
    • J. Karvanen and A. Cichocki, "Measuring sparseness of noisy signals," in Proc. ICA03, 2003.
    • (2003) Proc. ICA03
    • Karvanen, J.1    Cichocki, A.2
  • 31
    • 26844461512 scopus 로고    scopus 로고
    • Recovery of exact sparse representations in the presence of bounded noise
    • Oct
    • J. Fuchs, "Recovery of exact sparse representations in the presence of bounded noise," IEEE Trans. Inf. Theory, vol. 51, no. 10, pp. 3601-3608, Oct. 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.10 , pp. 3601-3608
    • Fuchs, J.1
  • 32
    • 33144483155 scopus 로고    scopus 로고
    • Stable recovery of sparse overcomplete representations in the presence of noise
    • Jan
    • D. Donoho, M. Elad, and V. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inf. Theory, vol. 52, no. 1, pp. 6-18, Jan. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.1 , pp. 6-18
    • Donoho, D.1    Elad, M.2    Temlyakov, V.3
  • 34
    • 33847752668 scopus 로고    scopus 로고
    • 1 norm iterative sparse solution for EEG source localization
    • Mar
    • 1 norm iterative sparse solution for EEG source localization," IEEE Trans. Biomed. Eng., vol. 54, no. 3, pp. 400-409, Mar. 2007.
    • (2007) IEEE Trans. Biomed. Eng , vol.54 , Issue.3 , pp. 400-409
    • Xu, P.1    Tian, Y.2    Chen, H.3    Yao, D.4
  • 35
    • 25444450826 scopus 로고    scopus 로고
    • Equivalence principle for optimization of sparse versus low-spread representations for signal estimation in noise
    • R. Balan, J. Rosca, and S. Rickard, "Equivalence principle for optimization of sparse versus low-spread representations for signal estimation in noise," Int. J. Imaging Syst. Technol., vol. 15, no. 1, pp. 10-17, 2005.
    • (2005) Int. J. Imaging Syst. Technol , vol.15 , Issue.1 , pp. 10-17
    • Balan, R.1    Rosca, J.2    Rickard, S.3
  • 36
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • Dec
    • E. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candes, E.1    Tao, T.2
  • 37
    • 55349134896 scopus 로고    scopus 로고
    • 1 -norm minimization problems when the solution may be sparse
    • Nov
    • 1 -norm minimization problems when the solution may be sparse," IEEE Trans. Inf. Theory vol. 54, no. 11, pp. 4789-4812, Nov. 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , Issue.11 , pp. 4789-4812
    • Donoho, D.1    Tsaig, Y.2
  • 38
    • 4043166218 scopus 로고    scopus 로고
    • Sparse coding of sensory inputs
    • Aug
    • B. A. Olshausen and D. J. Field, "Sparse coding of sensory inputs," Current Opin. Neurobiol., vol. 14, no. 4, pp. 481-487, Aug. 2004.
    • (2004) Current Opin. Neurobiol , vol.14 , Issue.4 , pp. 481-487
    • Olshausen, B.A.1    Field, D.J.2
  • 39
    • 0032712352 scopus 로고    scopus 로고
    • An affine scaling methodology for best basis selection
    • Jan
    • B. Rao and K. Kreutz-Delgado, "An affine scaling methodology for best basis selection," IEEE Trans. Signal Processing, vol. 47, pp. 187-200, Jan. 1999.
    • (1999) IEEE Trans. Signal Processing , vol.47 , pp. 187-200
    • Rao, B.1    Kreutz-Delgado, K.2
  • 40
    • 0031625511 scopus 로고    scopus 로고
    • Measures and algorithms for best basis selection
    • Seattle, WA
    • K. Kreutz-Delgado and B. Rao, "Measures and algorithms for best basis selection," in ICASSP1998, Seattle, WA, 1998.
    • (1998) ICASSP1998
    • Kreutz-Delgado, K.1    Rao, B.2
  • 41
    • 84900510076 scopus 로고    scopus 로고
    • Non-negative matrix factorization with sparseness constraints
    • P. O. Hoyer, "Non-negative matrix factorization with sparseness constraints," J. Mach. Learn. Res., vol. 5, pp. 1457-1469, 2004.
    • (2004) J. Mach. Learn. Res , vol.5 , pp. 1457-1469
    • Hoyer, P.O.1
  • 42
    • 25444498056 scopus 로고    scopus 로고
    • Sparse ICA for blind separation of transmitted and reflected images
    • A. Bronstein, M. Bronstein, M. Zibulevsky, and Y. Y. Zeevi, "Sparse ICA for blind separation of transmitted and reflected images," Int. J. Imag. Syst. Technol., vol. 15, no. 1, pp. 84-91, 2005.
    • (2005) Int. J. Imag. Syst. Technol , vol.15 , Issue.1 , pp. 84-91
    • Bronstein, A.1    Bronstein, M.2    Zibulevsky, M.3    Zeevi, Y.Y.4
  • 43
    • 84935761346 scopus 로고
    • Methods of measuring concentrations of wealth
    • M. O. Lorenz, "Methods of measuring concentrations of wealth," J. Amer. Stat. Assoc., 1905.
    • (1905) J. Amer. Stat. Assoc
    • Lorenz, M.O.1
  • 44
    • 0012057129 scopus 로고
    • Measurement of inequality of incomes
    • C. Gini, "Measurement of inequality of incomes," Econom. J., vol. 31, pp. 124-126, 1921.
    • (1921) Econom. J , vol.31 , pp. 124-126
    • Gini, C.1
  • 45
    • 14844312094 scopus 로고    scopus 로고
    • The mean-Gini efficient portfolio frontier
    • H. Shalit and S. Yitzhaki, "The mean-Gini efficient portfolio frontier," J. Finan. Res., vol. 28, no. 1, pp. 59-75, 2005.
    • (2005) J. Finan. Res , vol.28 , Issue.1 , pp. 59-75
    • Shalit, H.1    Yitzhaki, S.2
  • 46
    • 0035211240 scopus 로고    scopus 로고
    • Axiomatic characterization of the Gini coefficient and Lorenz curve orderings
    • R. Aaberge, "Axiomatic characterization of the Gini coefficient and Lorenz curve orderings," J. Econom. Theory, vol. 101, pp. 115-132, 2001.
    • (2001) J. Econom. Theory , vol.101 , pp. 115-132
    • Aaberge, R.1
  • 47
    • 70349618211 scopus 로고    scopus 로고
    • R. Aaberge, Erratum to axiomatic characterization of the Gini coefficient and Lorenz curve orderings, J. Econom. Theory, 140, no. 1, 2008.
    • R. Aaberge, "Erratum to axiomatic characterization of the Gini coefficient and Lorenz curve orderings," J. Econom. Theory, vol. 140, no. 1, 2008.
  • 48
    • 0031587251 scopus 로고    scopus 로고
    • A simpleway to calculate the Gini coefficient, and some implications
    • B. Milanovic, "A simpleway to calculate the Gini coefficient, and some implications," Econom. Lett., vol. 56, no. 1, pp. 45-49, 1997.
    • (1997) Econom. Lett , vol.56 , Issue.1 , pp. 45-49
    • Milanovic, B.1


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