메뉴 건너뛰기




Volumn 21, Issue 2, 2006, Pages 145-167

Fast and accurate Polar Fourier transform

Author keywords

Cartesian coordinates; Fast Fourier transform; Interpolation; Linogram; Polar coordinates; Pseudo Polar coordinates; Unequally sampled FFT

Indexed keywords

ALGORITHMS; ERROR ANALYSIS; INTERPOLATION; PROBLEM SOLVING;

EID: 33748181071     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2005.11.003     Document Type: Article
Times cited : (175)

References (42)
  • 1
    • 85008013248 scopus 로고    scopus 로고
    • Introduction the top 10 algorithms
    • Special issue
    • Dongarra J., and Sullivan F. Introduction the top 10 algorithms. Comput. Sci. Eng. 2 1 (2000) 22-79 Special issue
    • (2000) Comput. Sci. Eng. , vol.2 , Issue.1 , pp. 22-79
    • Dongarra, J.1    Sullivan, F.2
  • 3
    • 33748184510 scopus 로고    scopus 로고
    • A. Averbuch, R.R. Coifman, D.L. Donoho, M. Elad, M. Israeli, Accurate and fast Polar Fourier transform, in: The 37th Asilomar on Signals, Systems and Computers, Pacific Grove, CA, 2003
  • 6
    • 0021892209 scopus 로고
    • Comments on 'Direct Fourier reconstruction in computer tomography'
    • Fan H., and Sanz J.L.C. Comments on 'Direct Fourier reconstruction in computer tomography'. IEEE Trans. Acoust., Speech Signal Process. 33 2 (1985) 446-449
    • (1985) IEEE Trans. Acoust., Speech Signal Process. , vol.33 , Issue.2 , pp. 446-449
    • Fan, H.1    Sanz, J.L.C.2
  • 7
    • 33748137047 scopus 로고
    • Parallel implementation of the direct Fourier reconstruction method in tomography
    • Matej S., and Vajtersic M. Parallel implementation of the direct Fourier reconstruction method in tomography. Comput. Artificial Intelligence 9 4 (1990) 379-393
    • (1990) Comput. Artificial Intelligence , vol.9 , Issue.4 , pp. 379-393
    • Matej, S.1    Vajtersic, M.2
  • 8
    • 33748155914 scopus 로고    scopus 로고
    • K.J. Moraski, D.C. Munson Jr., Fast tomographic reconstruction using Chirp-Z interpolation, in: Proc. 25th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, IEEE Comput. Soc. Press, Los Alamitos, CA, 1991, pp. 1052-1056
  • 9
    • 0030151068 scopus 로고    scopus 로고
    • A fast and accurate Fourier algorithm for iterative parallel-beam tomography
    • Delaney A.H., and Bresler Y. A fast and accurate Fourier algorithm for iterative parallel-beam tomography. IEEE Trans. Image Process. 5 5 (1996) 740-753
    • (1996) IEEE Trans. Image Process. , vol.5 , Issue.5 , pp. 740-753
    • Delaney, A.H.1    Bresler, Y.2
  • 10
    • 0031701795 scopus 로고    scopus 로고
    • Direct-Fourier reconstruction in tomography and synthetic aperture radar
    • Choi H., and Munson Jr. D.C. Direct-Fourier reconstruction in tomography and synthetic aperture radar. Int. J. Imaging Systems Technol. 9 1 (1998) 1-13
    • (1998) Int. J. Imaging Systems Technol. , vol.9 , Issue.1 , pp. 1-13
    • Choi, H.1    Munson Jr., D.C.2
  • 11
    • 0033623973 scopus 로고    scopus 로고
    • Analysis of the direct Fourier method for computer tomography
    • Walden J. Analysis of the direct Fourier method for computer tomography. IEEE Trans. Medical Imaging 19 3 (2000) 211-222
    • (2000) IEEE Trans. Medical Imaging , vol.19 , Issue.3 , pp. 211-222
    • Walden, J.1
  • 14
    • 0034298607 scopus 로고    scopus 로고
    • 2 log n) filtered backprojection reconstruction algorithm for tomography
    • 2 log n) filtered backprojection reconstruction algorithm for tomography. IEEE Trans. Image Process. 9 10 (2000) 1769-1773
    • (2000) IEEE Trans. Image Process. , vol.9 , Issue.10 , pp. 1769-1773
    • Basu, S.1    Bresler, Y.2
  • 15
    • 0742289178 scopus 로고    scopus 로고
    • Non-equispaced fast Fourier transforms with applications to tomography
    • Fourmont K. Non-equispaced fast Fourier transforms with applications to tomography. J. Fourier Anal. Appl. 9 (2003) 431-450
    • (2003) J. Fourier Anal. Appl. , vol.9 , pp. 431-450
    • Fourmont, K.1
  • 16
    • 1942423550 scopus 로고    scopus 로고
    • Iterative tomographic image reconstruction using Fourier-based forward and back-projectors
    • Matej S., Fessler J.A., and Kazantsev I.G. Iterative tomographic image reconstruction using Fourier-based forward and back-projectors. IEEE Trans. Medical Imaging 23 4 (2004) 401-412
    • (2004) IEEE Trans. Medical Imaging , vol.23 , Issue.4 , pp. 401-412
    • Matej, S.1    Fessler, J.A.2    Kazantsev, I.G.3
  • 17
    • 0026140811 scopus 로고
    • A spectral method of characteristics for hyperbolic problems
    • Suli E., and Ware A. A spectral method of characteristics for hyperbolic problems. SIAM J. Numer. Anal. 28 2 (1991) 423-445
    • (1991) SIAM J. Numer. Anal. , vol.28 , Issue.2 , pp. 423-445
    • Suli, E.1    Ware, A.2
  • 18
    • 0001266583 scopus 로고
    • Multipole expansions and pseudospectral cardinal functions: A new generalization of the fast Fourier transform
    • Boyd J.P. Multipole expansions and pseudospectral cardinal functions: A new generalization of the fast Fourier transform. J. Comput. Phys. 103 2 (1992) 184-186
    • (1992) J. Comput. Phys. , vol.103 , Issue.2 , pp. 184-186
    • Boyd, J.P.1
  • 19
    • 0002777177 scopus 로고
    • A fast algorithm for Chebyshev, Fourier, and sinc interpolation onto an irregular grid
    • Boyd J.P. A fast algorithm for Chebyshev, Fourier, and sinc interpolation onto an irregular grid. J. Comput. Phys. 103 2 (1992) 243-257
    • (1992) J. Comput. Phys. , vol.103 , Issue.2 , pp. 243-257
    • Boyd, J.P.1
  • 20
    • 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. 2 (1995) 263-381
    • (1995) Appl. Comput. Harmon. , vol.2 , pp. 263-381
    • Beylkin, G.1
  • 21
    • 0001303146 scopus 로고    scopus 로고
    • Rapid computation of the discrete Fourier transform
    • Anderson C., and Dahleh M.D. Rapid computation of the discrete Fourier transform. SIAM J. Sci. Comput. 17 (1998) 913-919
    • (1998) SIAM J. Sci. Comput. , vol.17 , pp. 913-919
    • Anderson, C.1    Dahleh, M.D.2
  • 22
    • 0000527817 scopus 로고
    • Fast Fourier transforms for nonequispaced data
    • Dutt A., and Rokhlin V. Fast Fourier transforms for nonequispaced data. SIAM J. Sci. Comput. 14 (1993) 1368-1393
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1368-1393
    • Dutt, A.1    Rokhlin, V.2
  • 23
    • 0029207497 scopus 로고
    • Fast Fourier transforms for nonequispaced data II
    • Dutt A., and Rokhlin V. Fast Fourier transforms for nonequispaced data II. Appl. Comput. Harmon. Anal. 2 (1995) 85-100
    • (1995) Appl. Comput. Harmon. Anal. , vol.2 , pp. 85-100
    • Dutt, A.1    Rokhlin, V.2
  • 24
    • 0032301587 scopus 로고    scopus 로고
    • Fast approximate Fourier transform for irregularly spaced data
    • Ware A.F. Fast approximate Fourier transform for irregularly spaced data. SIAM Rev. 40 4 (1998) 838-856
    • (1998) SIAM Rev. , vol.40 , Issue.4 , pp. 838-856
    • Ware, A.F.1
  • 25
    • 0011937243 scopus 로고    scopus 로고
    • Fast Fourier transforms for nonequispaced data: A tutorial
    • Benedetto J.J., and Ferreira P. (Eds), Birkhäuser ch. 12
    • Potts D., Steidl G., and Tasche M. Fast Fourier transforms for nonequispaced data: A tutorial. In: Benedetto J.J., and Ferreira P. (Eds). Modern Sampling Theory: Mathematics and Application (2000), Birkhäuser 253-274 ch. 12
    • (2000) Modern Sampling Theory: Mathematics and Application , pp. 253-274
    • Potts, D.1    Steidl, G.2    Tasche, M.3
  • 26
    • 0033102416 scopus 로고    scopus 로고
    • Nonuniform fast Fourier transform
    • Duijndam A.J.W., and Schonewille M.A. Nonuniform fast Fourier transform. Geophysics 64 2 (1999) 539-551
    • (1999) Geophysics , vol.64 , Issue.2 , pp. 539-551
    • Duijndam, A.J.W.1    Schonewille, M.A.2
  • 27
    • 0033295052 scopus 로고    scopus 로고
    • The regular Fourier matrices and nonuniform fast Fourier transforms
    • Nguyen N., and Liu Q.H. The regular Fourier matrices and nonuniform fast Fourier transforms. SIAM J. Sci. Comput. 21 1 (1999) 283-293
    • (1999) SIAM J. Sci. Comput. , vol.21 , Issue.1 , pp. 283-293
    • Nguyen, N.1    Liu, Q.H.2
  • 28
    • 0037306521 scopus 로고    scopus 로고
    • Nonuniform fast Fourier transforms using min-max interpolation
    • Fessler J.A., and Sutton B.P. Nonuniform fast Fourier transforms using min-max interpolation. IEEE Trans. Signal Process. 51 2 (2003) 560-574
    • (2003) IEEE Trans. Signal Process. , vol.51 , Issue.2 , pp. 560-574
    • Fessler, J.A.1    Sutton, B.P.2
  • 29
    • 4944230740 scopus 로고    scopus 로고
    • Accelerating the nonuniform fast Fourier transform
    • Greengard L., and Lee J.Y. Accelerating the nonuniform fast Fourier transform. SIAM Rev. 46 (2004) 443-454
    • (2004) SIAM Rev. , vol.46 , pp. 443-454
    • Greengard, L.1    Lee, J.Y.2
  • 30
    • 33748198883 scopus 로고    scopus 로고
    • A. Averbuch, R. Coifman, D.L. Donoho, M. Israeli, Fast Slant Stack: A notion of Radon transform for data in a Cartesian grid which is rapidly computible, algebraically exact, geometrically faithful and invertible, Technical Report, Statistics Department, Stanford University, 2003
  • 31
    • 0016117351 scopus 로고
    • Digital reconstruction of multidimensional signals from their projections
    • Mersereau R.M., and Oppenheim A.V. Digital reconstruction of multidimensional signals from their projections. Proc. IEEE 62 10 (1974) 1319-1338
    • (1974) Proc. IEEE , vol.62 , Issue.10 , pp. 1319-1338
    • Mersereau, R.M.1    Oppenheim, A.V.2
  • 32
    • 33748186305 scopus 로고    scopus 로고
    • J.E. Pasciak, A note on the Fourier algorithm for image reconstruction, Preprint AMD 896, Applied Mathematics Department, Brookhaven National Laboratory, Upton, NY, 1981
  • 33
    • 0023669757 scopus 로고
    • Linograms in image reconstruction from projections
    • Edholm P., and Herman G.T. Linograms in image reconstruction from projections. IEEE Trans. Medical Imaging MI-6 4 (1987) 301-307
    • (1987) IEEE Trans. Medical Imaging , vol.MI-6 , Issue.4 , pp. 301-307
    • Edholm, P.1    Herman, G.T.2
  • 34
    • 0024034707 scopus 로고
    • A new Polar Fourier-transform for computer-aided tomography and spotlight synthetic aperture radar
    • Lawton W. A new Polar Fourier-transform for computer-aided tomography and spotlight synthetic aperture radar. IEEE Trans. Acoust., Speech Signal Process. 36 6 (1988) 931-933
    • (1988) IEEE Trans. Acoust., Speech Signal Process. , vol.36 , Issue.6 , pp. 931-933
    • Lawton, W.1
  • 36
    • 11844275989 scopus 로고    scopus 로고
    • A pseudoPolar FFT technique for translation, rotation and scale-invariant image registration
    • Keller Y., Averbuch A., and Israeli M. A pseudoPolar FFT technique for translation, rotation and scale-invariant image registration. IEEE Trans. Image Process. 14 1 (2005) 12-22
    • (2005) IEEE Trans. Image Process. , vol.14 , Issue.1 , pp. 12-22
    • Keller, Y.1    Averbuch, A.2    Israeli, M.3
  • 37
    • 3943055955 scopus 로고
    • The Chirp Z-transform algorithm and its application
    • Rabiner L.R., Schafer R.W., and Rader C.M. The Chirp Z-transform algorithm and its application. Bell System Tech. J. 48 (1969) 1249-1292
    • (1969) Bell System Tech. J. , vol.48 , pp. 1249-1292
    • Rabiner, L.R.1    Schafer, R.W.2    Rader, C.M.3
  • 38
    • 0026222570 scopus 로고
    • The fractional Fourier transform and applications
    • Bailey D.H., and Swarztrauber P.N. The fractional Fourier transform and applications. SIAM Rev. 33 3 (1991) 389-404
    • (1991) SIAM Rev. , vol.33 , Issue.3 , pp. 389-404
    • Bailey, D.H.1    Swarztrauber, P.N.2
  • 41
    • 0002649812 scopus 로고
    • WaveLab and Reproducible Research
    • Springer-Verlag, Berlin
    • Buckheit J., and Donoho D.L. WaveLab and Reproducible Research. Wavelets and Statistics (1995), Springer-Verlag, Berlin
    • (1995) Wavelets and Statistics
    • Buckheit, J.1    Donoho, D.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.