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Volumn 31, Issue 1-3, 2009, Pages 283-328

The geometry and the analytic properties of isotropic multiresolution analysis

Author keywords

3D data representations; 3D textures; Isotropic multiresolution; Isotropic wavelets; Rigid motion covariant representations; Steerability

Indexed keywords


EID: 67349188233     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-008-9111-6     Document Type: Article
Times cited : (41)

References (67)
  • 3
    • 42149155689 scopus 로고    scopus 로고
    • Isotropic multiresolution analysis for 3D-textures and applications in cardiovascular imaging
    • Van Der Ville, D., Goyal, V., Papadakis, M. (eds.)
    • Alexander, S.K., Azencott, R., Papadakis, M.: Isotropic multiresolution analysis for 3D-textures and applications in cardiovascular imaging. In: Van Der Ville, D., Goyal, V., Papadakis, M. (eds.) Wavelets XII, SPIE, vol. 6701, pp. 67011S-1-67011S-12 (2007)
    • (2007) Wavelets XII, SPIE , vol.6701
    • Alexander, S.K.1    Azencott, R.2    Papadakis, M.3
  • 5
    • 0031184910 scopus 로고    scopus 로고
    • 2) non séparables, à support compact et de régularité arbitrairement grande
    • 2) non séparables, à support compact et de régularité arbitrairement grande Comptes Rendus Académie des Sciences de Paris 325 17 20
    • (1997) Comptes Rendus Académie des Sciences de Paris , vol.325 , pp. 17-20
    • Ayache, A.1
  • 6
    • 0033481322 scopus 로고    scopus 로고
    • 2) of arbitrarily high regularity
    • 2) of arbitrarily high regularity Rev. Mat. Iberoam 15 15 1 37 58
    • (1999) Rev. Mat. Iberoam 15 , vol.15 , Issue.1 , pp. 37-58
    • Ayache, A.1
  • 7
    • 0038454380 scopus 로고    scopus 로고
    • Some Methods for Constructing Nonseparable, Orthonormal, Compactly Supported Wavelet Bases
    • DOI 10.1006/acha.2000.0325, PII S1063520300903257
    • A. Ayache 2001 Some methods for constructing non separable, orthonormal, compactly supported wavelet bases Appl. Comput. Harmon. Anal. 10 99 111 (Pubitemid 33674556)
    • (2001) Applied and Computational Harmonic Analysis , vol.10 , Issue.1 , pp. 99-111
    • Ayache, A.1
  • 10
    • 67349161202 scopus 로고    scopus 로고
    • The construction of d-dimensional multiresolution analysis frames
    • J.J. Benedetto J.R. Romero 2007 The construction of d-dimensional multiresolution analysis frames J. Appl. Func. Anal. 2 4 403 426
    • (2007) J. Appl. Func. Anal. , vol.2 , Issue.4 , pp. 403-426
    • Benedetto, J.J.1    Romero, J.R.2
  • 11
    • 0347486142 scopus 로고    scopus 로고
    • The Theory of Multiresolution Analysis Frames and Applications to Filter Banks
    • J.J. Benedetto S. Li 1998 The theory of multiresolution analysis frames and applications to filter banks Appl. Comput. Harmon. Anal. 5 389 427 (Pubitemid 128413156)
    • (1998) Applied and Computational Harmonic Analysis , vol.5 , Issue.4 , pp. 389-427
    • Benedetto, J.J.1    Li, S.2
  • 13
    • 30844447904 scopus 로고    scopus 로고
    • Frame isotropic multiresolution analysis for micro CT scans of coronary arteries
    • Papadakis, M., Laine, A., Unser, M. (eds.)
    • Bodmann, B.G., Papadakis, M., et al.: Frame isotropic multiresolution analysis for micro CT scans of coronary arteries. In: Papadakis, M., Laine, A., Unser, M. (eds.) Wavelets XI, SPIE, vol. 5914, pp. 59141O/1-12 (2005)
    • (2005) Wavelets XI, SPIE , vol.5914
    • Bodmann, B.G.1    Papadakis, M.2
  • 17
    • 0346727379 scopus 로고    scopus 로고
    • Ridgelets: A key to higher dimensional intermittency?
    • E.J. Candes D.L. Donoho 1999 Ridgelets: a key to higher dimensional intermittency? Phil. Trans. R. Soc. Lond. A 2495 2509
    • (1999) Phil. Trans. R. Soc. Lond. , pp. 2495-2509
    • Candes, E.J.1    Donoho, D.L.2
  • 20
    • 0022219575 scopus 로고
    • A spatial filtering approach to texture analysis
    • J.M. Coggins A.K. Jain 1985 A spatial filtering approach to texture analysis Pattern recogn. Lett. 3 3 195 203
    • (1985) Pattern Recogn. Lett. , vol.3 , Issue.3 , pp. 195-203
    • Coggins, J.M.1    Jain, A.K.2
  • 21
    • 0002118102 scopus 로고
    • Nonseparable bidimensional wavelet bases
    • A. Cohen I. Daubechies 1993 Nonseparable bidimensional wavelet bases Rev. Mat. Iberoam 9 51 137
    • (1993) Rev. Mat. Iberoam , vol.9 , pp. 51-137
    • Cohen, A.1    Daubechies, I.2
  • 22
    • 42149173071 scopus 로고    scopus 로고
    • A new family of rotation-covariant wavelets on the hexagonal lattice
    • Van Der Ville, D., Goyal, V., Papadakis, M. (eds.)
    • Condat, L., Forster-Heinlein, B., Van Der Ville, D.: A new family of rotation-covariant wavelets on the hexagonal lattice. In: Van Der Ville, D., Goyal, V., Papadakis, M. (eds.) Wavelets XII, SPIE, vol. 6701, pp. 67010B-1-67010B-9 (2007)
    • (2007) Wavelets XII, SPIE , vol.6701
    • Condat, L.1    Forster-Heinlein, B.2    Van Der Ville, D.3
  • 26
    • 0035277292 scopus 로고    scopus 로고
    • Nonseparable, Compactly Supported Interpolating Refinable Functions with Arbitrary Smoothness
    • DOI 10.1006/acha.2000.0334, PII S1063520300903348
    • J. Derado 2001 Nonseprable, compactly supported interpolating refinable functions with arbitrary smoothness Appl. Comput. Harmon. Anal. 10 2 113 138 (Pubitemid 33675430)
    • (2001) Applied and Computational Harmonic Analysis , vol.10 , Issue.2 , pp. 113-138
    • Derado, J.1
  • 27
    • 67349140108 scopus 로고    scopus 로고
    • Texture identification of tissues using directional wavelet, ridgelet and curvelet transforms
    • Larson, D.R., Massopust, P.R., Nashed, Z., Nguyen, M.-C., Papadakis, M., Zayed, A.I. (eds.) Contemp. Mathem., Amer. Math. Soc.
    • Dettori, L., Zayed, A.I.: Texture identification of tissues using directional wavelet, ridgelet and curvelet transforms. In: Larson, D.R., Massopust, P.R., Nashed, Z., Nguyen, M.-C., Papadakis, M., Zayed, A.I. (eds.) Frames and Operator Theory in Analysis and Signal Processing, Contemp. Mathem., Amer. Math. Soc., vol. 451, pp. 89-118 (2008)
    • (2008) Frames and Operator Theory in Analysis and Signal Processing , vol.451 , pp. 89-118
    • Dettori, L.1    Zayed, A.I.2
  • 29
    • 84951613222 scopus 로고
    • An almost orthogonal radial wavelet expansion for radial distributions
    • J. Epperson M. Frazier 1995 An almost orthogonal radial wavelet expansion for radial distributions J. Fourier Anal. Appl. 1 3 311 353
    • (1995) J. Fourier Anal. Appl. , vol.1 , Issue.3 , pp. 311-353
    • Epperson, J.1    Frazier, M.2
  • 30
    • 52849126063 scopus 로고    scopus 로고
    • Polar wavelets and associated Littlewood-Paley theory
    • J. Epperson M. Frazier 1996 Polar wavelets and associated Littlewood-Paley theory Diss. Math. 348 1 51
    • (1996) Diss. Math. , vol.348 , pp. 1-51
    • Epperson, J.1    Frazier, M.2
  • 31
    • 55849110030 scopus 로고    scopus 로고
    • Isotropic moments over integer lattices
    • M. Fickus D.G. Mixon 2009 Isotropic moments over integer lattices Appl. Comp. Harmon. Anal. 26 1 77 96
    • (2009) Appl. Comp. Harmon. Anal. , vol.26 , Issue.1 , pp. 77-96
    • Fickus, M.1    Mixon, D.G.2
  • 32
    • 42149085880 scopus 로고    scopus 로고
    • Multiscale moment transforms over the integer lattice
    • Van Der Ville, D., Goyal, V., Papadakis, M. (eds.)
    • Fickus, M., Seetharaman, G.S., Oxley, M.E.: Multiscale moment transforms over the integer lattice. In: Van Der Ville, D., Goyal, V., Papadakis, M. (eds.) Wavelets XII, SPIE, vol. 6701, pp. 67011N-1-67011N-8 (2007)
    • (2007) Wavelets XII, SPIE , vol.6701
    • Fickus, M.1    Seetharaman, G.S.2    Oxley, M.E.3
  • 37
    • 0026743540 scopus 로고
    • Multiresolution analysis, Haar bases and self-similar tilings
    • K. Grochenig W. Madych 1992 Multiresolution analysis, Haar bases and self-similar tilings IEEE Trans. Inf. Theory 38 558 568
    • (1992) IEEE Trans. Inf. Theory , vol.38 , pp. 558-568
    • Grochenig, K.1    Madych, W.2
  • 40
    • 57649135081 scopus 로고    scopus 로고
    • Examples of bivariate nonseparable compactly supported orthonormal continuous wavelets
    • Unser, M., Aldroubi, A., Laine, A. (eds.)
    • He, W., Lai, M.J.: Examples of bivariate nonseparable compactly supported orthonormal continuous wavelets. In: Unser, M., Aldroubi, A., Laine, A. (eds.) Wavelet Applications in Signal and Image Processing IV, Proceedings SPIE, vol. 3169, pp. 303-314 (1997)
    • (1997) Wavelet Applications in Signal and Image Processing IV, Proceedings SPIE , vol.3169 , pp. 303-314
    • He, W.1    Lai, M.J.2
  • 41
    • 0037646050 scopus 로고    scopus 로고
    • Integrated wavelets for enhancement of microcalcifications in digital mamography
    • P. Heinlein J. Drexl W. Schneider 2003 Integrated wavelets for enhancement of microcalcifications in digital mamography IEEE Trans. Med. Imag. 22 3 402 413
    • (2003) IEEE Trans. Med. Imag. , vol.22 , Issue.3 , pp. 402-413
    • Heinlein, P.1    Drexl, J.2    Schneider, W.3
  • 44
    • 67349244545 scopus 로고    scopus 로고
    • Explicit schemes in seismic migration and isotropic multiscale representations
    • Grinberg, E., Larson, D.R., Jorgensen, P.E.T., Massopust, P., Olafsson, G., Quinto, E.T., Rubin, B. (eds.)
    • Jain, S., Papadakis, M., Dussaud, E.: Explicit schemes in seismic migration and isotropic multiscale representations. In: Grinberg, E., Larson, D.R., Jorgensen, P.E.T., Massopust, P., Olafsson, G., Quinto, E.T., Rubin, B. (eds.) Radon Transforms, Geometry, and Wavelets, Contemp. Mathem., Amer. Math. Soc., vol. 464, pp. 177-200 (2008)
    • (2008) Radon Transforms, Geometry, and Wavelets, Contemp. Mathem., Amer. Math. Soc. , vol.464 , pp. 177-200
    • Jain, S.1    Papadakis, M.2    Dussaud, E.3
  • 45
    • 0029765168 scopus 로고    scopus 로고
    • A filter design technique for steerable pyramid image transforms
    • ICASP, Atlanta, GA
    • Karasaridis, A., Simoncelli, E.: A filter design technique for steerable pyramid image transforms. In: Acoustics Speech and Signal Processing, ICASP, Atlanta, GA (1996)
    • (1996) Acoustics Speech and Signal Processing
    • Karasaridis, A.1    Simoncelli, E.2
  • 46
    • 0346876959 scopus 로고    scopus 로고
    • Image processing with complex wavelets
    • N. Kingsbury 1999 Image processing with complex wavelets Phil. Trans. R. Soc. London A 357 2543 2560
    • (1999) Phil. Trans. R. Soc. London A , vol.357 , pp. 2543-2560
    • Kingsbury, N.1
  • 47
    • 0026624134 scopus 로고
    • Nonseparable multidimensional perfect reconstruction filter-banks
    • J. Kovačević M. Vetterli 1992 Nonseparable multidimensional perfect reconstruction filter-banks IEEE Trans. Inf. Theory 38 533 555
    • (1992) IEEE Trans. Inf. Theory , vol.38 , pp. 533-555
    • Kovačević, J.1    Vetterli, M.2
  • 48
    • 30844463689 scopus 로고    scopus 로고
    • Sparse multidimensional representation using shearlets
    • Papadakis, M., Laine, A., Unser, M. (eds.) January
    • Labate, D., Lim, W., Kutyniok, G., Weiss, G.: Sparse multidimensional representation using shearlets. In: Papadakis, M., Laine, A., Unser, M. (eds.) Wavelets XI, SPIE Proceedings, vol. 5914, pp. 247-255, January 2005
    • (2005) Wavelets XI, SPIE Proceedings , vol.5914 , pp. 247-255
    • Labate, D.1    Lim, W.2    Kutyniok, G.3    Weiss, G.4
  • 50
    • 51249193272 scopus 로고
    • Translation invariant spaces
    • P.D. Lax 1959 Translation invariant spaces Acta Math. 101 163 178
    • (1959) Acta Math. , vol.101 , pp. 163-178
    • Lax, P.D.1
  • 54
    • 0346750479 scopus 로고    scopus 로고
    • Frames of translates and the generalized frame multiresolution analysis
    • Kopotun, K., Lyche, T., Neamtu, M. (eds.) Vanderbilt University Press, Nashville, TN
    • Papadakis, M.: Frames of translates and the generalized frame multiresolution analysis. In: Kopotun, K., Lyche, T., Neamtu, M. (eds.) Trends in Approximation Theory, Innovations in Applied Mathematics, pp. 353-362. Vanderbilt University Press, Nashville, TN (2001)
    • (2001) Trends in Approximation Theory, Innovations in Applied Mathematics , pp. 353-362
    • Papadakis, M.1
  • 57
    • 0242636409 scopus 로고    scopus 로고
    • Image denoising using Gaussian scale mixtures in the wavelet domain
    • Computer Science Techn. Rep. nr. TR2002-831, Courant Institute of Mathematical Sciences
    • Portilla, J., Strela, V., Wainwright, M.J., Simoncelli, E.P.: Image denoising using Gaussian scale mixtures in the wavelet domain. In: IEEE Trans. Image Processing, vol.12(11), pp. 1338-1351. Computer Science Techn. Rep. nr. TR2002-831, Courant Institute of Mathematical Sciences (2003)
    • (2003) IEEE Trans. Image Processing , vol.12 , Issue.11 , pp. 1338-1351
    • Portilla, J.1    Strela, V.2    Wainwright, M.J.3    Simoncelli, E.P.4
  • 59
    • 0031571549 scopus 로고    scopus 로고
    • d ): The analysis of the Analysis operator
    • d ): the analysis of the Analysis operator J. Func. Anal. 148 408 447
    • (1997) J. Func. Anal. , vol.148 , pp. 408-447
    • Ron, A.1    Shen, Z.2
  • 60
    • 0035276530 scopus 로고    scopus 로고
    • Smooth Wavelet Tight Frames with Zero Moments
    • DOI 10.1006/acha.2000.0332, PII S1063520300903324
    • I.W. Selesnick 2001 Smooth wavelet tight frames with zero moments Appl. Comput. Harmon. Anal. 10 2 163 181 (Pubitemid 33675432)
    • (2001) Applied and Computational Harmonic Analysis , vol.10 , Issue.2 , pp. 163-181
    • Selesnick, I.W.1
  • 63
    • 30844471763 scopus 로고    scopus 로고
    • Morphological component analysis
    • Papadakis, M., Laine, A.F., Unser, M. (eds.)
    • Starck, J.-L., Moudden, Y., Bobin, J., Elad, M., Donoho, D.L.: Morphological component analysis. In: Papadakis, M., Laine, A.F., Unser, M. (eds.) Wavelets XI, SPIE, vol. 5914, pp. 59140Q-1-59140Q-15 (2005)
    • (2005) Wavelets XI, SPIE , vol.5914
    • Starck, J.-L.1    Moudden, Y.2    Bobin, J.3    Elad, M.4    Donoho, D.L.5
  • 64
    • 33747690437 scopus 로고    scopus 로고
    • Rotation-invariant texture retrieval with gaussianized steerable pyramids
    • DOI 10.1109/TIP.2006.877356
    • G. Tzagkarakis B. Beferull-Lozano P. Tsakalides 2006 Rotation-invariant texture retrieval with Gaussianized steerable pyramids IEEE Trans. Image Process 15 9 2702 2718 (Pubitemid 44270211)
    • (2006) IEEE Transactions on Image Processing , vol.15 , Issue.9 , pp. 2702-2718
    • Tzagkarakis, G.1    Beferull-Lozano, B.2    Tsakalides, P.3


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