메뉴 건너뛰기




Volumn 61, Issue 13, 2013, Pages 3357-3367

Tight wavelet frames on multislice graphs

Author keywords

Higher order singular value decomposition (HOSVD); Multislice graph; Spectral graph theory; Tensor decompositions; Wavelet transform

Indexed keywords

FUNCTIONAL MAGNETIC RESONANCE IMAGING; HIGHER ORDER SINGULAR VALUE DECOMPOSITION (HOSVD); MATRIX FACTORIZATIONS; MULTI SLICES; MULTI-LINEAR ALGEBRAS; SPECTRAL GRAPH THEORY; TENSOR DECOMPOSITION; TIGHT WAVELET FRAMES;

EID: 84879108392     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2013.2259825     Document Type: Article
Times cited : (130)

References (42)
  • 1
    • 77952328459 scopus 로고    scopus 로고
    • Community structure in time-dependent, multiscale, and multiplex networks
    • May
    • P. J. Mucha, T. Richardson, K. Macon, M. A. Porter, and J.-P. Onnela, "Community structure in time-dependent, multiscale, and multiplex networks," Science, vol. 328, no. 5980, pp. 876-878, May 2010.
    • (2010) Science , vol.328 , Issue.5980 , pp. 876-878
    • Mucha, P.J.1    Richardson, T.2    MacOn, K.3    Porter, M.A.4    Onnela, J.-P.5
  • 3
    • 77956372873 scopus 로고    scopus 로고
    • Multirelational organization of large-scale social networks in an online world
    • Jul
    • M. Szell, R. Lambiotte, and S. Thurner, "Multirelational organization of large-scale social networks in an online world," Proc. Natl. Acad. Sci. USA, vol. 107, no. 31, pp. 13636-13641, Jul. 2010.
    • (2010) Proc. Natl. Acad. Sci. USA , vol.107 , Issue.31 , pp. 13636-13641
    • Szell, M.1    Lambiotte, R.2    Thurner, S.3
  • 4
    • 77951126500 scopus 로고    scopus 로고
    • Catastrophic cascade of failures in interdependent networks
    • Apr
    • S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, and S. Havlin, "Catastrophic cascade of failures in interdependent networks," Nature, vol. 464, no. 7291, pp. 1025-1028, Apr. 2010.
    • (2010) Nature , vol.464 , Issue.7291 , pp. 1025-1028
    • Buldyrev, S.V.1    Parshani, R.2    Paul, G.3    Stanley, H.E.4    Havlin, S.5
  • 6
    • 58149333658 scopus 로고    scopus 로고
    • Multiscale methods for data on graphs and irregular multidimensional situations
    • Jan
    • M. Jansen, G. P. Nason, and B.W. Silverman, "Multiscale methods for data on graphs and irregular multidimensional situations," J. R. Stat. Soc. Ser. B Stat. Methodol., vol. 71, no. 1, pp. 97-125, Jan. 2009.
    • (2009) J. R. Stat. Soc. Ser. B Stat. Methodol , vol.71 , Issue.1 , pp. 97-125
    • Jansen, M.1    Nason, G.P.2    Silverman, B.W.3
  • 7
    • 80051723858 scopus 로고    scopus 로고
    • Generalized tree-based wavelet transform
    • Sep
    • I. Ram, M. Elad, and I. Cohen, "Generalized tree-based wavelet transform," IEEE Trans. Signal Process., vol. 59, pp. 4199-4209, Sep. 2011.
    • (2011) IEEE Trans. Signal Process , vol.59 , pp. 4199-4209
    • Ram, I.1    Elad, M.2    Cohen, I.3
  • 10
    • 84861117945 scopus 로고    scopus 로고
    • Perfect reconstruction two-channel wavelet filter banks for graph structured data
    • Jun
    • S. K. Narang and A. Ortega, "Perfect reconstruction two-channel wavelet filter banks for graph structured data," IEEE Trans. Signal Process., vol. 60, pp. 2786-2799, Jun. 2012.
    • (2012) IEEE Trans. Signal Process , vol.60 , pp. 2786-2799
    • Narang, S.K.1    Ortega, A.2
  • 11
    • 0030813663 scopus 로고    scopus 로고
    • Parafac tutorial and applications
    • R. Bro, "Parafac tutorial and applications," Chem. Intell. Lab. Syst., vol. 38, pp. 149-171, 1997.
    • (1997) Chem. Intell. Lab. Syst , vol.38 , pp. 149-171
    • Bro, R.1
  • 12
    • 0019635684 scopus 로고
    • Strategies for analyzing data from video fluorometric monitoring of liquid chromatographic effluents
    • C. J. Appellof and E. R. Davidson, "Strategies for analyzing data from video fluorometric monitoring of liquid chromatographic effluents," Anal. Chem., vol. 53, no. 13, pp. 2053-2056, 1981.
    • (1981) Anal. Chem , vol.53 , Issue.13 , pp. 2053-2056
    • Appellof, C.J.1    Davidson, E.R.2
  • 13
    • 84944415516 scopus 로고    scopus 로고
    • Multilinear analysis of image ensembles: Tensorfaces
    • Copenhagen
    • M. A. O. Vasilescu and D. Terzopoulos, "Multilinear analysis of image ensembles: Tensorfaces," in Proc. Eur. Conf. Comput. Vis., Copenhagen, 2002, pp. 447-460.
    • (2002) Proc. Eur. Conf. Comput. Vis , pp. 447-460
    • Vasilescu, M.A.O.1    Terzopoulos, D.2
  • 14
    • 68649096448 scopus 로고    scopus 로고
    • Tensor decompositions and applications
    • Aug
    • T. G. Kolda and B. W. Bader, "Tensor decompositions and applications," SIAM Rev., vol. 51, no. 3, pp. 455-500, Aug. 2009.
    • (2009) SIAM Rev , vol.51 , Issue.3 , pp. 455-500
    • Kolda, T.G.1    Bader, B.W.2
  • 15
    • 0013953617 scopus 로고
    • Some mathematical notes of three-mode factor analysis
    • L. Tucker, "Some mathematical notes of three-mode factor analysis," Psychometrika, vol. 31, pp. 279-311, 1966.
    • (1966) Psychometrika , vol.31 , pp. 279-311
    • Tucker, L.1
  • 17
    • 34250499792 scopus 로고
    • Analysis of individual differences in multidimensional scaling via an n-way generalization of eckart-young decomposition
    • J. D. Carroll and J.-J. Chang, "Analysis of individual differences in multidimensional scaling via an n-way generalization of eckart-young decomposition," Psychometrika, vol. 35, pp. 283-319, 1970.
    • (1970) Psychometrika , vol.35 , pp. 283-319
    • Carroll, J.D.1    Chang, J.-J.2
  • 18
    • 0002740437 scopus 로고
    • Foundations of the PARAFAC procedure: Models and conditions for an explanatory multi-modal factor analysis
    • R. Harshman, "Foundations of the PARAFAC procedure: Models and conditions for an explanatory multi-modal factor analysis," UCLA Working Papers in Phonetics, vol. 16, no. 1, pp. 1-84, 1970.
    • (1970) UCLA Working Papers in Phonetics , vol.16 , Issue.1 , pp. 1-84
    • Harshman, R.1
  • 20
    • 0037212207 scopus 로고    scopus 로고
    • Finite normalized tight frames
    • J. Benedetto and M. Fickus, "Finite normalized tight frames," Adv. Comput. Math., vol. 18, no. 2, pp. 357-385, 2003.
    • (2003) Adv. Comput. Math , vol.18 , Issue.2 , pp. 357-385
    • Benedetto, J.1    Fickus, M.2
  • 21
    • 0003737944 scopus 로고
    • Principe d'incertitude, bases Hilbertiennes et algèbres d'opérateurs
    • (in French)
    • Y. Meyer, "Principe d'incertitude, bases Hilbertiennes et algèbres d'opérateurs," in Seminaire Bourbaki (in French), 1986, vol. 662, pp. 209-223.
    • (1986) Seminaire Bourbaki , vol.662 , pp. 209-223
    • Meyer, Y.1
  • 22
    • 0034291204 scopus 로고    scopus 로고
    • A parametric texture model based on joint statistics of complex wavelet coefficients
    • Oct
    • J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int. J. Comput. Vis., vol. 40, pp. 49-70, Oct. 2000.
    • (2000) Int. J. Comput. Vis , vol.40 , pp. 49-70
    • Portilla, J.1    Simoncelli, E.P.2
  • 23
    • 67349188233 scopus 로고    scopus 로고
    • The geometry and the analytic properties of isotropic multiresolution analysis
    • J. Romero, S. Alexander, S. Baid, S. Jain, and M. Papadakis, "The geometry and the analytic properties of isotropic multiresolution analysis," Adv. Comput. Math., vol. 31, pp. 283-328, 2009.
    • (2009) Adv. Comput. Math , vol.31 , pp. 283-328
    • Romero, J.1    Alexander, S.2    Baid, S.3    Jain, S.4    Papadakis, M.5
  • 24
  • 25
    • 0003168357 scopus 로고
    • Wavelet bases for with rational dilation factor
    • Boston, MA, USA: Jones and Bartlett
    • P. Auscher, "Wavelet bases for with rational dilation factor," in Wavelets and Their Applications. Boston, MA, USA: Jones and Bartlett, 1992, pp. 439-451.
    • (1992) Wavelets and Their Applications , pp. 439-451
    • Auscher, P.1
  • 26
    • 4444318027 scopus 로고    scopus 로고
    • Rational multiresolution analysis and fast wavelet transform: Application to wavelet shrinkage denoising
    • Aug
    • A. Baussard, F. Nicolier, and F. Truchetet, "Rational multiresolution analysis and fast wavelet transform: application to wavelet shrinkage denoising," Signal Process., vol. 84, no. 10, pp. 1735-1747, Aug. 2004.
    • (2004) Signal Process , vol.84 , Issue.10 , pp. 1735-1747
    • Baussard, A.1    Nicolier, F.2    Truchetet, F.3
  • 27
    • 0000044932 scopus 로고    scopus 로고
    • The discrete cosine transform
    • Aug
    • G. Strang, "The discrete cosine transform," SIAM Rev., vol. 41, no. 1, pp. 135-147, Aug. 1999.
    • (1999) SIAM Rev , vol.41 , Issue.1 , pp. 135-147
    • Strang, G.1
  • 28
    • 0036083440 scopus 로고    scopus 로고
    • Stretch vs slice methods for representing three-way structure via matrix notation
    • Apr
    • R. Harshman and S. Hong, "'Stretch' vs 'slice' methods for representing three-way structure via matrix notation," J. Chemometrics, vol. 16, no. 4, pp. 198-205, Apr. 2002.
    • (2002) J. Chemometrics , vol.16 , Issue.4 , pp. 198-205
    • Harshman, R.1    Hong, S.2
  • 30
    • 0034144761 scopus 로고    scopus 로고
    • On the best rank-1 and rank-) approximation of higher-order tensors
    • Mar
    • L. De Lathauwer, B. De Moor, and J. Vandewalle, "On the best rank-1 and rank-) approximation of higher-order tensors," SIAM J. Matrix Anal. Appl., vol. 21, no. 4, pp. 1324-1342, Mar. 2000.
    • (2000) SIAM J. Matrix Anal. Appl , vol.21 , Issue.4 , pp. 1324-1342
    • De Lathauwer, L.1    De Moor, B.2    Vandewalle, J.3
  • 31
    • 0022557697 scopus 로고
    • A note on the gradient of a multi-image
    • Jan
    • S. Di Zenzo, "A note on the gradient of a multi-image," Comput. Vis. Graph. Image Process., vol. 33, no. 1, pp. 116-125, Jan. 1986.
    • (1986) Comput. Vis. Graph. Image Process , vol.33 , Issue.1 , pp. 116-125
    • Di Zenzo, S.1
  • 33
    • 79955472817 scopus 로고    scopus 로고
    • Understanding complexity in the human brain
    • May
    • D. S. Bassett and M. S. Gazzaniga, "Understanding complexity in the human brain," Trends Cogn. Sci., vol. 15, no. 5, pp. 200-209, May 2011.
    • (2011) Trends Cogn. Sci , vol.15 , Issue.5 , pp. 200-209
    • Bassett, D.S.1    Gazzaniga, M.S.2
  • 34
    • 75249093217 scopus 로고    scopus 로고
    • Time-frequency dynamics of resting-state brain connectivity measured with fMRI
    • Mar
    • C. Chang and G. H. Glover, "Time-frequency dynamics of resting-state brain connectivity measured with fMRI," Neuro Image, vol. 50, no. 1, pp. 81-98, Mar. 2010.
    • (2010) Neuro Image , vol.50 , Issue.1 , pp. 81-98
    • Chang, C.1    Glover, G.H.2
  • 35
    • 78650189468 scopus 로고    scopus 로고
    • Impact of transient emotions on functional connectivity during subsequent resting state: A wavelet correlation approach
    • Oct
    • H. Eryilmaz, D. V. D. Ville, S. Schwartz, and P. Vuilleumier, "Impact of transient emotions on functional connectivity during subsequent resting state: A wavelet correlation approach," Neuro Image, vol. 54, no. 3, pp. 2481-2491, Oct. 2011.
    • (2011) Neuro Image , vol.54 , Issue.3 , pp. 2481-2491
    • Eryilmaz, H.1    Ville, D.V.D.2    Schwartz, S.3    Vuilleumier, P.4
  • 37
    • 0036322886 scopus 로고    scopus 로고
    • Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain
    • Jan
    • N. Tzourio-Mazoyer, B. Landeau, D. Papathanassiou, F. Crivello, O. Etard, N. Delcroix, B. Mazoyer, and M. Joliot, "Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain," Neuro Image, vol. 15, no. 1, pp. 273-289, Jan. 2002.
    • (2002) Neuro Image , vol.15 , Issue.1 , pp. 273-289
    • Tzourio-Mazoyer, N.1    Landeau, B.2    Papathanassiou, D.3    Crivello, F.4    Etard, O.5    Delcroix, N.6    Mazoyer, B.7    Joliot, M.8
  • 38
    • 80055054102 scopus 로고    scopus 로고
    • Wavelet frames on graphs defined by fMRI functional connectivity
    • Chicago, IL, USA
    • N. Leonardi and D. Van De Ville, "Wavelet frames on graphs defined by fMRI functional connectivity," in Proc. IEEE Int. Symp. Biomed. Imag., Chicago, IL, USA, 2011, pp. 2136-2139.
    • (2011) Proc. IEEE Int. Symp. Biomed. Imag , pp. 2136-2139
    • Leonardi, N.1    Van De Ville, D.2
  • 39
    • 84874990386 scopus 로고    scopus 로고
    • Discrete signal processing on graphs
    • Apr
    • A. Sandryhaila and J. M. F. Moura, "Discrete signal processing on graphs," IEEE Trans. Signal Process., vol. 61, no. 7, pp. 1644-1656, Apr. 2013.
    • (2013) IEEE Trans. Signal Process , vol.61 , Issue.7 , pp. 1644-1656
    • Sandryhaila, A.1    Moura, J.M.F.2
  • 40
    • 0000187741 scopus 로고
    • A characteristic equation associated to an eigenvalue problem on -networks
    • J. von Below, "A characteristic equation associated to an eigenvalue problem on -networks," Linear Algebra Appl., vol. 71, pp. 309-325, 1985.
    • (1985) Linear Algebra Appl , vol.71 , pp. 309-325
    • Von Below, J.1
  • 41
    • 0000746335 scopus 로고    scopus 로고
    • The spectrum of the continuous Laplacian on a graphs
    • C. Cattaneo, "The spectrum of the continuous Laplacian on a graphs," Monatshefte fuer Mathematik, vol. 124, pp. 215-235, 1997.
    • (1997) Monatshefte fuer Mathematik , vol.124 , pp. 215-235
    • Cattaneo, C.1
  • 42
    • 8744284618 scopus 로고    scopus 로고
    • Wave equations for graphs and the edgebased Laplacian
    • J. Friedman and J.-P. Tillich, "Wave equations for graphs and the edgebased Laplacian," Pacific J. Math., vol. 216, pp. 229-266, 2004.
    • (2004) Pacific J. Math , vol.216 , pp. 229-266
    • Friedman, J.1    Tillich, J.-P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.