메뉴 건너뛰기




Volumn 36, Issue 2, 2014, Pages 183-197

Harmonic singular integrals and steerable wavelets in L 2 ( Rd)

Author keywords

Singular integrals; Spherical harmonics; Steerable wavelets

Indexed keywords

ANGULAR DECOMPOSITION; COMPUTATIONALLY EFFICIENT; FOURIER MULTIPLIERS; MOTHER WAVELETS; SINGULAR INTEGRAL; SPATIAL DOMAINS; SPHERICAL HARMONICS; STEERABLE WAVELETS;

EID: 84893021533     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2013.03.006     Document Type: Article
Times cited : (21)

References (32)
  • 1
    • 68649091969 scopus 로고    scopus 로고
    • A survey on spherical designs and algebraic combinatorics on spheres
    • Ei. Bannai, and Et. Bannai A survey on spherical designs and algebraic combinatorics on spheres European J. Combin. 30 6 2009 1392 1425
    • (2009) European J. Combin. , vol.30 , Issue.6 , pp. 1392-1425
    • Bannai, Ei.1    Bannai, Et.2
  • 2
    • 84856002833 scopus 로고    scopus 로고
    • Special Functions
    • Cambridge University Press Cambridge
    • R. Beals, and R. Wong Special Functions Cambridge Stud. Adv. Math. vol. 126 2010 Cambridge University Press Cambridge
    • (2010) Cambridge Stud. Adv. Math. , vol.126 VOL.
    • Beals, R.1    Wong, R.2
  • 3
    • 0000024746 scopus 로고
    • Singular integral operators and differential equations
    • A.P. Calderón, and A. Zygmund Singular integral operators and differential equations Amer. J. Math. 79 1957 901 921
    • (1957) Amer. J. Math. , vol.79 , pp. 901-921
    • Calderón, A.P.1    Zygmund, A.2
  • 6
    • 0003601390 scopus 로고    scopus 로고
    • Constructive Approximation on the Sphere
    • The Clarendon Press, Oxford University Press New York
    • W. Freeden, T. Gervens, and M. Schreiner Constructive Approximation on the Sphere Numer. Math. Sci. Comput. 1998 The Clarendon Press, Oxford University Press New York
    • (1998) Numer. Math. Sci. Comput.
    • Freeden, W.1    Gervens, T.2    Schreiner, M.3
  • 7
    • 0033427780 scopus 로고    scopus 로고
    • Constructive approximation and numerical methods in geodetic research today - An attempt at a categorization based on an uncertainty principle
    • W. Freeden, and V. Michel Constructive approximation and numerical methods in geodetic research today - an attempt at a categorization based on an uncertainty principle J. Geodesy 73 1999 452 465 (Pubitemid 30042256)
    • (1999) Journal of Geodesy , vol.73 , Issue.9 , pp. 452-465
    • Freeden, W.1    Michel, V.2
  • 10
    • 84892967000 scopus 로고
    • Series of orthogonal polynomials
    • D. Jackson Series of orthogonal polynomials Ann. of Math. (2) 34 3 1933 527 545
    • (1933) Ann. of Math. (2) , vol.34 , Issue.3 , pp. 527-545
    • Jackson, D.1
  • 12
    • 79960738892 scopus 로고    scopus 로고
    • Optimally localized approximate identities on the 2-sphere
    • V. Michel Optimally localized approximate identities on the 2-sphere Numer. Funct. Anal. Optim. 32 8 2011 877 903
    • (2011) Numer. Funct. Anal. Optim. , vol.32 , Issue.8 , pp. 877-903
    • Michel, V.1
  • 13
    • 0004063533 scopus 로고
    • Translated from Russian by W.J.A. Whyte. Translation edited by I.N. Sneddon Pergamon Press Oxford
    • S.G. Mikhlin Multidimensional Singular Integrals and Integral Equations Translated from Russian by W.J.A. Whyte. Translation edited by I.N. Sneddon 1965 Pergamon Press Oxford
    • (1965) Multidimensional Singular Integrals and Integral Equations
    • Mikhlin, S.G.1
  • 14
    • 0003360039 scopus 로고
    • Spherical Harmonics
    • Springer-Verlag Berlin
    • C. Müller Spherical Harmonics Lecture Notes in Math. vol. 17 1966 Springer-Verlag Berlin
    • (1966) Lecture Notes in Math. , vol.17 VOL.
    • Müller, C.1
  • 15
    • 0003334981 scopus 로고    scopus 로고
    • Analysis of Spherical Symmetries in Euclidean Spaces
    • Springer-Verlag New York
    • C. Müller Analysis of Spherical Symmetries in Euclidean Spaces Appl. Math. Sci. vol. 129 1998 Springer-Verlag New York
    • (1998) Appl. Math. Sci. , vol.129 VOL.
    • Müller, C.1
  • 17
    • 0040251195 scopus 로고    scopus 로고
    • Nonstationary wavelets on the m-sphere for scattered data
    • DOI 10.1006/acha.1996.0025
    • F.J. Narcowich, and J.D. Ward Nonstationary wavelets on the m-sphere for scattered data Appl. Comput. Harmon. Anal. 3 4 1996 324 336 (Pubitemid 126366104)
    • (1996) Applied and Computational Harmonic Analysis , vol.3 , Issue.4 , pp. 324-336
    • Narcowich, F.J.1    Ward, J.D.2
  • 18
    • 0034291204 scopus 로고    scopus 로고
    • A parametric texture model based on joint statistics of complex wavelet coefficients
    • J. Portilla, and E.P. Simoncelli A parametric texture model based on joint statistics of complex wavelet coefficients Int. J. Comput. Vis. 40 2000 49 70
    • (2000) Int. J. Comput. Vis. , vol.40 , pp. 49-70
    • Portilla, J.1    Simoncelli, E.P.2
  • 19
    • 0001878701 scopus 로고
    • Positive definite functions on spheres
    • I.J. Schoenberg Positive definite functions on spheres Duke Math. J. 9 1942 96 108
    • (1942) Duke Math. J. , vol.9 , pp. 96-108
    • Schoenberg, I.J.1
  • 20
    • 21444439543 scopus 로고    scopus 로고
    • On a new condition for strictly positive definite functions on spheres
    • M. Schreiner On a new condition for strictly positive definite functions on spheres Proc. Amer. Math. Soc. 125 2 1997 531 540 (Pubitemid 127038790)
    • (1997) Proceedings of the American Mathematical Society , vol.125 , Issue.2 , pp. 531-540
    • Schreiner, M.1
  • 21
    • 48549108193 scopus 로고
    • Averaging sets: A generalization of mean values and spherical designs
    • P.D. Seymour, and T. Zaslavsky Averaging sets: a generalization of mean values and spherical designs Adv. Math. 52 3 1984 213 240
    • (1984) Adv. Math. , vol.52 , Issue.3 , pp. 213-240
    • Seymour, P.D.1    Zaslavsky, T.2
  • 22
    • 79956318853 scopus 로고    scopus 로고
    • Slepian functions and their use in signal estimation and spectral analysis
    • Willi Freeden, M. Zuhair Nashed, Thomas Sonar, Springer Berlin, Heidelberg
    • F.J. Simons Slepian functions and their use in signal estimation and spectral analysis Willi Freeden, M. Zuhair Nashed, Thomas Sonar, Handbook of Geomathematics 2010 Springer Berlin, Heidelberg 891 923
    • (2010) Handbook of Geomathematics , pp. 891-923
    • Simons, F.J.1
  • 23
    • 33746171197 scopus 로고    scopus 로고
    • Spatiospectral concentration on a sphere
    • DOI 10.1137/S0036144504445765
    • F.J. Simons, F.A. Dahlen, and M.A. Wieczorek Spatiospectral concentration on a sphere SIAM Rev. 48 3 2006 504 536 (electronic) (Pubitemid 44335973)
    • (2006) SIAM Review , vol.48 , Issue.3 , pp. 504-536
    • Simons, F.J.1    Dahlen, F.A.2    Wieczorek, M.A.3
  • 24
    • 0003201639 scopus 로고
    • Singular Integrals and Differentiability Properties of Functions
    • Princeton University Press Princeton, NJ
    • E.M. Stein Singular Integrals and Differentiability Properties of Functions Princeton Math. Ser. vol. 30 1970 Princeton University Press Princeton, NJ
    • (1970) Princeton Math. Ser. , vol.30 VOL.
    • Stein, E.M.1
  • 25
    • 0003207103 scopus 로고
    • Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
    • Princeton University Press Princeton, NJ
    • E.M. Stein Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals Princeton Math. Ser. vol. 43 1993 Princeton University Press Princeton, NJ
    • (1993) Princeton Math. Ser. , vol.43 VOL.
    • Stein, E.M.1
  • 26
    • 0003263410 scopus 로고
    • Introduction to Fourier Analysis on Euclidean Spaces
    • Princeton University Press Princeton, NJ
    • E.M. Stein, and G. Weiss Introduction to Fourier Analysis on Euclidean Spaces Princeton Math. Ser. vol. 32 1971 Princeton University Press Princeton, NJ
    • (1971) Princeton Math. Ser. , vol.32 VOL.
    • Stein, E.M.1    Weiss, G.2
  • 27
    • 84875890422 scopus 로고    scopus 로고
    • A unifying parametric framework for 2D steerable wavelet transforms
    • M. Unser, and N. Chenouard A unifying parametric framework for 2D steerable wavelet transforms SIAM J. Imaging Sci. 6 1 2013 102 135
    • (2013) SIAM J. Imaging Sci. , vol.6 , Issue.1 , pp. 102-135
    • Unser, M.1    Chenouard, N.2
  • 29
    • 77249087202 scopus 로고    scopus 로고
    • Wavelet steerability and the higher-order Riesz transform
    • M. Unser, and D. Van de Ville Wavelet steerability and the higher-order Riesz transform IEEE Trans. Image Process. 19 3 2010 636 652
    • (2010) IEEE Trans. Image Process. , vol.19 , Issue.3 , pp. 636-652
    • Unser, M.1    Van De Ville, D.2
  • 31
    • 26644435618 scopus 로고    scopus 로고
    • Scattered Data Approximation
    • Cambridge University Press Cambridge
    • H. Wendland Scattered Data Approximation Cambridge Monogr. Appl. Comput. Math. vol. 17 2005 Cambridge University Press Cambridge
    • (2005) Cambridge Monogr. Appl. Comput. Math. , vol.17 VOL.
    • Wendland, H.1
  • 32
    • 84966231566 scopus 로고
    • Strictly positive definite functions on spheres
    • Y. Xu, and E.W. Cheney Strictly positive definite functions on spheres Proc. Amer. Math. Soc. 116 4 1992 977 981
    • (1992) Proc. Amer. Math. Soc. , vol.116 , Issue.4 , pp. 977-981
    • Xu, Y.1    Cheney, E.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.