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Volumn 30, Issue 2, 2011, Pages 129-150

Wavelets on graphs via spectral graph theory

Author keywords

Graph theory; Overcomplete wavelet frames; Spectral graph theory; Wavelets

Indexed keywords

CHEBYSHEV POLYNOMIAL APPROXIMATION; FOURIER DOMAINS; GRAPH LAPLACIAN; INDICATOR FUNCTIONS; LOCALIZATION PROPERTIES; NOVEL METHODS; OVER-COMPLETE; POTENTIAL APPLICATIONS; PROBLEM DOMAIN; SCALE PARAMETER; SPECTRAL DECOMPOSITION; SPECTRAL GRAPH THEORY; WAVELETS; WEIGHTED GRAPH;

EID: 78751582295     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2010.04.005     Document Type: Article
Times cited : (2195)

References (57)
  • 1
    • 0027798110 scopus 로고
    • Embedded image coding using zerotrees of wavelet coefficients
    • J. Shapiro Embedded image coding using zerotrees of wavelet coefficients IEEE Trans. Signal Process. 41 12 1993 3445 3462
    • (1993) IEEE Trans. Signal Process. , vol.41 , Issue.12 , pp. 3445-3462
    • Shapiro, J.1
  • 2
    • 0030173121 scopus 로고    scopus 로고
    • A new, fast, and efficient image codec based on set partitioning in hierarchical trees
    • A. Said, and W. Pearlman A new, fast, and efficient image codec based on set partitioning in hierarchical trees IEEE Trans. Circuits Syst. Video Technol. 6 3 1996 243 250
    • (1996) IEEE Trans. Circuits Syst. Video Technol. , vol.6 , Issue.3 , pp. 243-250
    • Said, A.1    Pearlman, W.2
  • 3
    • 0030947878 scopus 로고    scopus 로고
    • Wavelet and wavelet packet compression of electrocardiograms
    • M. Hilton Wavelet and wavelet packet compression of electrocardiograms IEEE Trans. Biomed. Eng. 44 5 1997 394 402
    • (1997) IEEE Trans. Biomed. Eng. , vol.44 , Issue.5 , pp. 394-402
    • Hilton, M.1
  • 4
    • 0033338289 scopus 로고    scopus 로고
    • Image compression via joint statistical characterization in the wavelet domain
    • R. Buccigrossi, and E. Simoncelli Image compression via joint statistical characterization in the wavelet domain IEEE Trans. Image Process. 8 12 1999 1688 1701
    • (1999) IEEE Trans. Image Process. , vol.8 , Issue.12 , pp. 1688-1701
    • Buccigrossi, R.1    Simoncelli, E.2
  • 6
    • 0041958932 scopus 로고
    • Ideal spatial adaptation by wavelet shrinkage
    • D.L. Donoho, and I.M. Johnstone Ideal spatial adaptation by wavelet shrinkage Biometrika 81 1994 425 455
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.L.1    Johnstone, I.M.2
  • 7
    • 0034258869 scopus 로고    scopus 로고
    • Adaptive wavelet thresholding for image denoising and compression
    • S. Chang, B. Yu, and M. Vetterli Adaptive wavelet thresholding for image denoising and compression IEEE Trans. Image Process. 9 9 2000 1532 1546
    • (2000) IEEE Trans. Image Process. , vol.9 , Issue.9 , pp. 1532-1546
    • Chang, S.1    Yu, B.2    Vetterli, M.3
  • 8
    • 0036844073 scopus 로고    scopus 로고
    • Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency
    • L. Sendur, and I. Selesnick Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency IEEE Trans. Signal Process. 50 11 2002 2744 2756
    • (2002) IEEE Trans. Signal Process. , vol.50 , Issue.11 , pp. 2744-2756
    • Sendur, L.1    Selesnick, I.2
  • 10
    • 20144365032 scopus 로고    scopus 로고
    • Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising
    • I. Daubechies, and G. Teschke Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising Appl. Comput. Harmon. Anal. 19 1 2005 1 16
    • (2005) Appl. Comput. Harmon. Anal. , vol.19 , Issue.1 , pp. 1-16
    • Daubechies, I.1    Teschke, G.2
  • 11
    • 0028372050 scopus 로고
    • Filtering and deconvolution by the wavelet transform
    • J.-L. Starck, and A. Bijaoui Filtering and deconvolution by the wavelet transform Signal Process. 35 3 1994 195 211
    • (1994) Signal Process. , vol.35 , Issue.3 , pp. 195-211
    • Starck, J.-L.1    Bijaoui, A.2
  • 12
    • 0029288068 scopus 로고
    • Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
    • D.L. Donoho Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition Appl. Comput. Harmon. Anal. 2 2 1995 101 126
    • (1995) Appl. Comput. Harmon. Anal. , vol.2 , Issue.2 , pp. 101-126
    • Donoho, D.L.1
  • 13
    • 0029290067 scopus 로고
    • A multiscale approach to sensor fusion and the solution of linear inverse problems
    • E. Miller, and A.S. Willsky A multiscale approach to sensor fusion and the solution of linear inverse problems Appl. Comput. Harmon. Anal. 2 2 1995 127 147
    • (1995) Appl. Comput. Harmon. Anal. , vol.2 , Issue.2 , pp. 127-147
    • Miller, E.1    Willsky, A.S.2
  • 14
    • 0034246021 scopus 로고    scopus 로고
    • A statistical multiscale framework for Poisson inverse problems
    • R. Nowak, and E. Kolaczyk A statistical multiscale framework for Poisson inverse problems IEEE Trans. Inform. Theory 46 5 2000 1811 1825
    • (2000) IEEE Trans. Inform. Theory , vol.46 , Issue.5 , pp. 1811-1825
    • Nowak, R.1    Kolaczyk, E.2
  • 15
    • 33645136947 scopus 로고    scopus 로고
    • Bayesian wavelet-based image deconvolution: A GEM algorithm exploiting a class of heavy-tailed priors
    • J. Bioucas-Dias Bayesian wavelet-based image deconvolution: A GEM algorithm exploiting a class of heavy-tailed priors IEEE Trans. Image Process. 15 4 2006 937 951
    • (2006) IEEE Trans. Image Process. , vol.15 , Issue.4 , pp. 937-951
    • Bioucas-Dias, J.1
  • 16
    • 0042341519 scopus 로고    scopus 로고
    • Rotation and scale invariant texture features using discrete wavelet packet transform
    • R. Manthalkar, P.K. Biswas, and B.N. Chatterji Rotation and scale invariant texture features using discrete wavelet packet transform Pattern Recognit. Lett. 24 14 2003 2455 2462
    • (2003) Pattern Recognit. Lett. , vol.24 , Issue.14 , pp. 2455-2462
    • Manthalkar, R.1    Biswas, P.K.2    Chatterji, B.N.3
  • 17
    • 0026628466 scopus 로고
    • Wavelet analysis and synthesis of fractional Brownian motion
    • P. Flandrin Wavelet analysis and synthesis of fractional Brownian motion IEEE Trans. Inform. Theory 38 2 1992 910 917 (Part 2)
    • (1992) IEEE Trans. Inform. Theory , vol.38 , Issue.2 , pp. 910-917
    • Flandrin, P.1
  • 19
    • 0028461417 scopus 로고
    • Automated learning of decision rules for text categorization
    • C. Apté, F. Damerau, and S.M. Weiss Automated learning of decision rules for text categorization ACM Trans. Inf. Syst. 12 3 1994 233 251
    • (1994) ACM Trans. Inf. Syst. , vol.12 , Issue.3 , pp. 233-251
    • Apté, C.1    Damerau, F.2    Weiss, S.M.3
  • 20
  • 22
    • 0020737631 scopus 로고
    • The Laplacian pyramid as a compact image code
    • P.J. Burt, and E.H. Adelson The Laplacian pyramid as a compact image code IEEE Trans. Commun. 31 4 1983 532 540
    • (1983) IEEE Trans. Commun. , vol.31 , Issue.4 , pp. 532-540
    • Burt, P.J.1    Adelson, E.H.2
  • 24
    • 0035331869 scopus 로고    scopus 로고
    • Complex wavelets for shift invariant analysis and filtering of signals
    • N. Kingsbury Complex wavelets for shift invariant analysis and filtering of signals Appl. Comput. Harmon. Anal. 10 3 2001 234 253
    • (2001) Appl. Comput. Harmon. Anal. , vol.10 , Issue.3 , pp. 234-253
    • Kingsbury, N.1
  • 25
    • 2442458882 scopus 로고    scopus 로고
    • New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities
    • E. Candes, and D. Donoho New tight frames of curvelets and optimal representations of objects with piecewise C 2 singularities Comm. Pure Appl. Math. 57 2003 219 266
    • (2003) Comm. Pure Appl. Math. , vol.57 , pp. 219-266
    • Candes, E.1    Donoho, D.2
  • 26
    • 52349096502 scopus 로고    scopus 로고
    • Orthogonal bandlet bases for geometric images approximation
    • G. Peyré, and S. Mallat Orthogonal bandlet bases for geometric images approximation Comm. Pure Appl. Math. 61 9 2008 1173 1212
    • (2008) Comm. Pure Appl. Math. , vol.61 , Issue.9 , pp. 1173-1212
    • Peyré, G.1    Mallat, S.2
  • 27
    • 0043242765 scopus 로고    scopus 로고
    • Wavelets on the 2-sphere: A group-theoretical approach
    • J. Antoine, and P. Vandergheynst Wavelets on the 2-sphere: A group-theoretical approach Appl. Comput. Harmon. Anal. 7 3 1999 262 291
    • (1999) Appl. Comput. Harmon. Anal. , vol.7 , Issue.3 , pp. 262-291
    • Antoine, J.1    Vandergheynst, P.2
  • 31
    • 67149123578 scopus 로고    scopus 로고
    • Graph wavelet alignment kernels for drug virtual screening
    • A. Smalter, J. Huan, and G. Lushington Graph wavelet alignment kernels for drug virtual screening J. Bioinform. Comput. Biol. 7 2009 473 497
    • (2009) J. Bioinform. Comput. Biol. , vol.7 , pp. 473-497
    • Smalter, A.1    Huan, J.2    Lushington, G.3
  • 32
    • 58149333658 scopus 로고    scopus 로고
    • Multiscale methods for data on graphs and irregular multidimensional situations
    • 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. 71 1 2009 97 125
    • (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
  • 33
    • 34250832748 scopus 로고    scopus 로고
    • The Haar wavelet transform of a dendrogram
    • F. Murtagh The Haar wavelet transform of a dendrogram J. Classification 24 1 2007 3 32
    • (2007) J. Classification , vol.24 , Issue.1 , pp. 3-32
    • Murtagh, F.1
  • 34
    • 66549093404 scopus 로고    scopus 로고
    • Treelets an adaptive multi-scale basis for sparse unordered data
    • A.B. Lee, B. Nadler, and L. Wasserman Treelets an adaptive multi-scale basis for sparse unordered data Ann. Appl. Stat. 2 2008 435 471
    • (2008) Ann. Appl. Stat. , vol.2 , pp. 435-471
    • Lee, A.B.1    Nadler, B.2    Wasserman, L.3
  • 36
    • 41349101092 scopus 로고    scopus 로고
    • Diffusion polynomial frames on metric measure spaces
    • M. Maggioni, and H. Mhaskar Diffusion polynomial frames on metric measure spaces Appl. Comput. Harmon. Anal. 24 3 2008 329 353
    • (2008) Appl. Comput. Harmon. Anal. , vol.24 , Issue.3 , pp. 329-353
    • Maggioni, M.1    Mhaskar, H.2
  • 37
    • 67651027819 scopus 로고    scopus 로고
    • Continuous wavelets on compact manifolds
    • D. Geller, and A. Mayeli Continuous wavelets on compact manifolds Math. Z. 262 2009 895 927
    • (2009) Math. Z. , vol.262 , pp. 895-927
    • Geller, D.1    Mayeli, A.2
  • 38
    • 0000562670 scopus 로고
    • Decomposition of Hardy functions into square integrable wavelets of constant shape
    • A. Grossmann, and J. Morlet Decomposition of Hardy functions into square integrable wavelets of constant shape SIAM J. Math. Anal. 15 4 1984 723 736
    • (1984) SIAM J. Math. Anal. , vol.15 , Issue.4 , pp. 723-736
    • Grossmann, A.1    Morlet, J.2
  • 39
    • 26944489604 scopus 로고    scopus 로고
    • From graphs to manifolds - Weak and strong pointwise consistency of graph Laplacians
    • Proc. 18th Conf. Learning Theory (COLT)
    • M. Hein, J. Audibert, and U. von Luxburg From graphs to manifolds - weak and strong pointwise consistency of graph Laplacians P. Auer, R. Meir, Proc. 18th Conf. Learning Theory (COLT) Lecture Notes in Comput. Sci. vol. 3559 2005 Springer-Verlag 470 485
    • (2005) Lecture Notes in Comput. Sci. , vol.3559 , pp. 470-485
    • Hein, M.1    Audibert, J.2    Von Luxburg, U.3
  • 40
    • 33745397832 scopus 로고    scopus 로고
    • From graph to manifold Laplacian: The convergence rate
    • A. Singer From graph to manifold Laplacian: The convergence rate Appl. Comput. Harmon. Anal. 21 1 2006 128 134 diffusion maps and wavelets
    • (2006) Appl. Comput. Harmon. Anal. , vol.21 , Issue.1 , pp. 128-134
    • Singer, A.1
  • 41
    • 55449104028 scopus 로고    scopus 로고
    • Towards a theoretical foundation for Laplacian-based manifold methods
    • M. Belkin, and P. Niyogi Towards a theoretical foundation for Laplacian-based manifold methods J. Comput. System Sci. 74 8 2008 1289 1308 learning theory, 2005
    • (2008) J. Comput. System Sci. , vol.74 , Issue.8 , pp. 1289-1308
    • Belkin, M.1    Niyogi, P.2
  • 43
  • 44
    • 0024903928 scopus 로고
    • Continuous and discrete wavelet transforms
    • C.E. Heil, and D.F. Walnut Continuous and discrete wavelet transforms SIAM Rev. 31 4 1989 628 666
    • (1989) SIAM Rev. , vol.31 , Issue.4 , pp. 628-666
    • Heil, C.E.1    Walnut, D.F.2
  • 46
    • 0030560293 scopus 로고    scopus 로고
    • A Jacobi-Davidson iteration method for linear eigenvalue problems
    • G.L.G. Sleijpen, and H.A.V. der Vorst A Jacobi-Davidson iteration method for linear eigenvalue problems SIAM J. Matrix Anal. Appl. 17 2 1996 401 425
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , Issue.2 , pp. 401-425
    • Sleijpen, G.L.G.1    Der Vorst, H.A.V.2
  • 48
    • 33746258270 scopus 로고
    • A survey of methods of computing minimax and near-minimax polynomial approximations for functions of a single independent variable
    • W. Fraser A survey of methods of computing minimax and near-minimax polynomial approximations for functions of a single independent variable J. Assoc. Comput. Mach. 12 1965 295 314
    • (1965) J. Assoc. Comput. Mach. , vol.12 , pp. 295-314
    • Fraser, W.1
  • 49
    • 0003503811 scopus 로고
    • Near-minimax polynomial approximation in an elliptical region
    • K.O. Geddes Near-minimax polynomial approximation in an elliptical region SIAM J. Numer. Anal. 15 6 1978 1225 1233
    • (1978) SIAM J. Numer. Anal. , vol.15 , Issue.6 , pp. 1225-1233
    • Geddes, K.O.1
  • 50
    • 26844461332 scopus 로고    scopus 로고
    • Interpolation and Approximation by Polynomials
    • Springer-Verlag
    • G.M. Phillips Interpolation and Approximation by Polynomials CMS Books Math. 2003 Springer-Verlag
    • (2003) CMS Books Math.
    • Phillips, G.M.1
  • 51
    • 0027815286 scopus 로고
    • Acceleration of the frame algorithm
    • K. Grochenig Acceleration of the frame algorithm IEEE Trans. Signal Process. 41 12 1993 3331 3340
    • (1993) IEEE Trans. Signal Process. , vol.41 , Issue.12 , pp. 3331-3340
    • Grochenig, K.1
  • 52
    • 0033989015 scopus 로고    scopus 로고
    • Complex denoising of MR data via wavelet analysis: Application for functional MRI
    • S. Zaroubi, and G. Goelman Complex denoising of MR data via wavelet analysis: Application for functional MRI Magnetic Resonance Imaging 18 1 2000 59 68
    • (2000) Magnetic Resonance Imaging , vol.18 , Issue.1 , pp. 59-68
    • Zaroubi, S.1    Goelman, G.2
  • 54
    • 13844309282 scopus 로고    scopus 로고
    • Integrated wavelet processing and spatial statistical testing of fMRI data
    • D.V.D. Ville, T. Blu, and M. Unser Integrated wavelet processing and spatial statistical testing of fMRI data Neuroimage 23 4 2004 1472 1485
    • (2004) Neuroimage , vol.23 , Issue.4 , pp. 1472-1485
    • Ville, D.V.D.1    Blu, T.2    Unser, M.3
  • 56
    • 0029749195 scopus 로고    scopus 로고
    • A global, self-consistent, hierarchical, high-resolution shoreline database
    • P. Wessel, and W.H.F. Smith A global, self-consistent, hierarchical, high-resolution shoreline database J. Geophys. Res. 101 B4 1996 8741 8743 http://www.ngdc.noaa.gov/mgg/shorelines/gshhs.html
    • (1996) J. Geophys. Res. , vol.101 , Issue.B4 , pp. 8741-8743
    • Wessel, P.1    Smith, W.H.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.