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Volumn 52, Issue 3, 2009, Pages 355-384

A fast algorithm for nonequispaced Fourier transforms on the rotation group

Author keywords

Fast discrete transforms; Fast Fourier transform at nonequispaced nodes; Fourier synthesis; Generalized spherical harmonics; Rotation group; Spherical Fourier transform; Wigner D functions; Wigner d functions

Indexed keywords


EID: 70350400724     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-009-9277-0     Document Type: Article
Times cited : (48)

References (32)
  • 1
    • 0040844860 scopus 로고    scopus 로고
    • Fast polynomial multiplication and convolution related to the discrete cosine transform
    • Baszenski, G., Tasche, M.: Fast polynomial multiplication and convolution related to the discrete cosine transform. Linear Algebra Appl. 252, 1-25 (1997).
    • (1997) Linear Algebra Appl. , vol.252 , pp. 1-25
    • Baszenski, G.1    Tasche, M.2
  • 2
    • 3142776518 scopus 로고
    • On the fast Fourier transform of functions with singularities
    • Beylkin, G.: On the fast Fourier transform of functions with singularities. Appl. Comput. Harmon. Anal. 2, 363-381 (1995).
    • (1995) Appl. Comput. Harmon. Anal. , vol.2 , pp. 363-381
    • Beylkin, G.1
  • 7
    • 0000273884 scopus 로고
    • Computing Fourier transforms and convolutions on the 2-sphere
    • Driscoll, J.R., Healy, D.: Computing Fourier transforms and convolutions on the 2-sphere. Adv. Appl. Math. 15, 202-250 (1994).
    • (1994) Adv. Appl. Math. , vol.15 , pp. 202-250
    • Driscoll, J.R.1    Healy, D.2
  • 8
    • 0000527817 scopus 로고
    • Fast Fourier transforms for nonequispaced data
    • Dutt, A., Rokhlin, V.: Fast Fourier transforms for nonequispaced data. SIAM J. Sci. Stat. Comput. 14, 1368-1393 (1993).
    • (1993) SIAM J. Sci. Stat. Comput. , vol.14 , pp. 1368-1393
    • Dutt, A.1    Rokhlin, V.2
  • 10
    • 52149107219 scopus 로고    scopus 로고
    • Stability results for scattered data interpolation on the rotation group
    • Gräf, M., Kunis, S.: Stability results for scattered data interpolation on the rotation group. Electron. Trans. Numer. Anal. 31, 30-39 (2008).
    • (2008) Electron. Trans. Numer. Anal. , vol.31 , pp. 30-39
    • Gräf, M.1    Kunis, S.2
  • 12
    • 42549103049 scopus 로고    scopus 로고
    • The Radon transform on SO(3): A Fourier slice theorem and numerical inversion
    • Hielscher, R., Potts, D., Prestin, J., Schaeben, H., Schmalz, M.: The Radon transform on SO(3): a Fourier slice theorem and numerical inversion. Inverse Probl. 24, 025011 (2008).
    • (2008) Inverse Probl. , vol.24 , pp. 025011
    • Hielscher, R.1    Potts, D.2    Prestin, J.3    Schaeben, H.4    Schmalz, M.5
  • 15
    • 38849204845 scopus 로고    scopus 로고
    • Fast evaluation of quadrature formulae on the sphere
    • Keiner, J., Potts, D.: Fast evaluation of quadrature formulae on the sphere. Math. Comput. 77, 397-419 (2008).
    • (2008) Math. Comput. , vol.77 , pp. 397-419
    • Keiner, J.1    Potts, D.2
  • 17
    • 0242626807 scopus 로고    scopus 로고
    • Fast spherical Fourier algorithms
    • Kunis, S., Potts, D.: Fast spherical Fourier algorithms. J. Comput. Appl. Math. 161, 75-98 (2003).
    • (2003) J. Comput. Appl. Math. , vol.161 , pp. 75-98
    • Kunis, S.1    Potts, D.2
  • 20
    • 0347511542 scopus 로고    scopus 로고
    • A fast transform for spherical harmonics
    • Mohlenkamp, M.J.: A fast transform for spherical harmonics. J. Fourier Anal. Appl. 5, 159-184 (1999).
    • (1999) J. Fourier Anal. Appl. , vol.5 , pp. 159-184
    • Mohlenkamp, M.J.1
  • 21
    • 0032367851 scopus 로고    scopus 로고
    • Fast algorithms for discrete polynomial transforms
    • Potts, D., Steidl, G., Tasche, M.: Fast algorithms for discrete polynomial transforms. Math. Comput. 67, 1577-1590 (1998).
    • (1998) Math. Comput. , vol.67 , pp. 1577-1590
    • Potts, D.1    Steidl, G.2    Tasche, M.3
  • 22
    • 0032365169 scopus 로고    scopus 로고
    • Fast and stable algorithms for discrete spherical Fourier transforms
    • Potts, D., Steidl, G., Tasche, M.: Fast and stable algorithms for discrete spherical Fourier transforms. Linear Algebra Appl. 275/276, 433-450 (1998).
    • (1998) Linear Algebra Appl. , vol.275-276 , pp. 433-450
    • Potts, D.1    Steidl, G.2    Tasche, M.3
  • 23
    • 0011937243 scopus 로고    scopus 로고
    • Fast Fourier transforms for nonequispaced data: A tutorial
    • J. J. Benedetto and PJSGFerreira (Eds.), Boston: Birkhäuser
    • Potts, D., Steidl, G., Tasche, M.: Fast Fourier transforms for nonequispaced data: a tutorial. In: Benedetto, J.J., Ferreira, P.J.S.G. (eds.), Modern Sampling Theory: Mathematics and Applications, pp. 247-270. Birkhäuser, Boston (2001).
    • (2001) Modern Sampling Theory: Mathematics and Applications , pp. 247-270
    • Potts, D.1    Steidl, G.2    Tasche, M.3
  • 24
    • 53449086253 scopus 로고    scopus 로고
    • Numerical stability of fast trigonometric transforms - a worst case study
    • Potts, D., Steidl, G., Tasche, M.: Numerical stability of fast trigonometric transforms - a worst case study. J. Concrete Appl. Math. 1, 1-36 (2003).
    • (2003) J. Concrete Appl. Math. , vol.1 , pp. 1-36
    • Potts, D.1    Steidl, G.2    Tasche, M.3
  • 26
    • 0029730011 scopus 로고    scopus 로고
    • Fourier transform summation of Legendre series and D-Functions
    • Risbo, T.: Fourier transform summation of Legendre series and D-Functions. J. Geod. 70, 383-396 (1996).
    • (1996) J. Geod. , vol.70 , pp. 383-396
    • Risbo, T.1
  • 27
    • 33751218044 scopus 로고    scopus 로고
    • Fast algorithms for spherical harmonic expansions
    • Rokhlin, V., Tygert, M.: Fast algorithms for spherical harmonic expansions. SIAM J. Sci. Comput. 27, 1903-1928 (2006).
    • (2006) SIAM J. Sci. Comput. , vol.27 , pp. 1903-1928
    • Rokhlin, V.1    Tygert, M.2
  • 28
    • 0042973792 scopus 로고    scopus 로고
    • Spherical harmonics in texture analysis
    • Schaeben, H., Boogaart, K.G.v.d.: Spherical harmonics in texture analysis. Tectonophysics 370, 253-268 (2003).
    • (2003) Tectonophysics , vol.370 , pp. 253-268
    • Schaeben, H.1    Boogaart, K.G.V.D.2
  • 29
    • 52149106897 scopus 로고    scopus 로고
    • Marcinkiewicz-Zygmund inequalities and polynomial approximation from scattered data on SO(3)
    • Schmid, D.: Marcinkiewicz-Zygmund inequalities and polynomial approximation from scattered data on SO(3). Numer. Funct. Anal. Optim. 29, 855-882 (2008).
    • (2008) Numer. Funct. Anal. Optim. , vol.29 , pp. 855-882
    • Schmid, D.1
  • 30
    • 0036013529 scopus 로고    scopus 로고
    • A fast spherical harmonics transform algorithm
    • Suda, R., Takami, M.: A fast spherical harmonics transform algorithm. Math. Comput. 71, 703-715 (2002).
    • (2002) Math. Comput. , vol.71 , pp. 703-715
    • Suda, R.1    Takami, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.