Bibliography

1

C. Anderson and M. Dahleh.
Rapid computation of the discrete Fourier transform.
SIAM J. Sci. Comput., 17:913 - 919, 1996.

2

F. Andersson and G. Beylkin.
The fast Gauss transform with complex parameters.
J. Comput. Physics, 203:274 - 286, 2005.

3

A. Averbuch, R. Coifman, D. L. Donoho, M. Elad, and M. Israeli.
Fast and accurate polar Fourier transform.
Appl. Comput. Harmon. Anal., 21:145 - 167, 2006.

4

R. F. Bass and K. Gröchenig.
Random sampling of multivariate trigonometric polynomials.
SIAM J. Math. Anal., 36:773 - 795, 2004.

5

R. K. Beatson and L. Greengard.
A short course on fast multipole methods.
In M. Ainsworth, J. Levesley, W. A. Light, and M. Marletta, editors, Wavelets, Multilevel Methods and Elliptic PDEs. Clarendon Press, 1997.

6

P. J. Beatty, D. G. Nishimura, and J. M. Pauly.
Rapid gridding reconstruction with a minimal oversampling ratio.
IEEE Trans. Med. Imag., 24:799 - 808, 2005.

7

G. Beylkin.
On the fast Fourier transform of functions with singularities.
Appl. Comput. Harmon. Anal., 2:363 - 381, 1995.

8

Å. Björck.
Numerical Methods for Least Squares Problems.
SIAM, Philadelphia, 1996.

9

H.-J. Bungartz and M. Griebel.
Sparse grids.
Acta Numer., 13:147 - 269, 2004.

10

E. J. Candes, L. Demanet, D. L. Donoho, and L. Ying.
Fast discrete curvelet transforms.
SIAM Multiscale Model. Simul., 3:861 - 899, 2006.

11

D. Donoho, A. Maleki, and M. Shaharam.
Wavelab 850.
http://www-stat.stanford.edu/$\sim$ wavelab, 2006.

12

J. R. Driscoll and D. Healy.
Computing Fourier transforms and convolutions on the 2-sphere.
Adv. in Appl. Math., 15:202 - 250, 1994.

13

J. R. Driscoll, D. Healy, and D. Rockmore.
Fast discrete polynomial transforms with applications to data analysis for distance transitive graphs.
SIAM J. Comput., 26:1066 - 1099, 1996.

14

A. J. W. Duijndam and M. A. Schonewille.
Nonuniform fast Fourier transform.
Geophysics, 64:539 - 551, 1999.

15

A. Dutt and V. Rokhlin.
Fast Fourier transforms for nonequispaced data.
SIAM J. Sci. Stat. Comput., 14:1368 - 1393, 1993.

16

A. Dutt and V. Rokhlin.
Fast Fourier transforms for nonequispaced data II.
Appl. Comput. Harmon. Anal., 2:85 - 100, 1995.

17

H. Eggers, T. Knopp, and D. Potts.
Field inhomogeneity correction based on gridding reconstruction.
Preprint 06-10, TU-Chemnitz, 2006.

18

B. Elbel and G. Steidl.
Fast Fourier transform for nonequispaced data.
In C. K. Chui and L. L. Schumaker, editors, Approximation Theory IX, Nashville, 1998. Vanderbilt University Press.

19

H. G. Feichtinger, K. Gröchenig, and T. Strohmer.
Efficient numerical methods in non-uniform sampling theory.
Numer. Math., 69:423 - 440, 1995.

20

M. Fenn, S. Kunis, and D. Potts.
Fast evaluation of trigonometric polynomials from hyperbolic crosses.
Numer. Algorithms, 41:339 - 352, 2006.

21

M. Fenn, S. Kunis, and D. Potts.
On the computation of the polar FFT.
Appl. Comput. Harmon. Anal., to appear.

22

M. Fenn and D. Potts.
Fast summation based on fast trigonometric transforms at nonequispaced nodes.
Numer. Linear Algebra Appl., 12:161 - 169, 2005.

23

M. Fenn and G. Steidl.
Fast NFFT based summation of radial functions.
Sampling Theory in Signal and Image Processing, 3:1 - 28, 2004.

24

J. A. Fessler and B. P. Sutton.
Nonuniform fast Fourier transforms using min-max interpolation.
IEEE Trans. Signal Process., 51:560 - 574, 2003.

25

K. Fourmont.
Schnelle Fourier-Transformation bei nichtäquidistanten Gittern und tomographische Anwendungen.
Dissertation, Universität Münster, 1999.

26

K. Fourmont.
Non equispaced fast Fourier transforms with applications to tomography.
J. Fourier Anal. Appl., 9:431 - 450, 2003.

27

R. Franke.
http://www.math.nps.navy.mil/$\sim$ rfranke/README.

28

M. Frigo and S. G. Johnson.
FFTW, C subroutine library.
http://www.fftw.org.

29

L. Greengard and J.-Y. Lee.
Accelerating the nonuniform fast Fourier transform.
SIAM Rev., 46:443 - 454, 2004.

30

J. I. Jackson, C. H. Meyer, D. G. Nishimura, and A. Macovski.
Selection of a convolution function for Fourier inversion using gridding.
IEEE Trans. Med. Imag., 10:473 - 478, 1991.

31

J. Keiner, S. Kunis, and D. Potts.
Fast summation of Radial Functions on the Sphere.
Computing, 78:1-15, 2006.

32

J. Keiner and D. Potts.
Fast evaluation of quadrature formulae on the sphere.
Preprint A-06-07, Universität zu Lübeck, 2006.

33

T. Knopp, S. Kunis, and D. Potts.
Fast iterative reconstruction for MRI from nonuniform k-space data.
revised Preprint A-05-10, Universität zu Lübeck, 2005.

34

S. Kunis and D. Potts.
Fast spherical Fourier algorithms.
J. Comput. Appl. Math., 161:75 - 98, 2003.

35

S. Kunis and D. Potts.
Stability results for scattered data interpolation by trigonometric polynomials.
revised Preprint A-04-12, Universität zu Lübeck, 2004.

36

S. Kunis and D. Potts.
Time and memory requirements of the nonequispaced FFT.
Preprint 06-01, TU-Chemnitz, 2006.

37

S. Kunis, D. Potts, and G. Steidl.
Fast Gauss transform with complex parameters using NFFTs.
J. Numer. Math., to appear.

38

J.-Y. Lee and L. Greengard.
The type 3 nonuniform FFT and its applications.
J. Comput. Physics, 206:1 - 5, 2005.

39

J. Ma and M. Fenn.
Combined complex ridgelet shrinkage and total variation minimization.
SIAM J. Sci. Comput., 28:984-1000, 2006.

40

N. Nguyen and Q. H. Liu.
The regular Fourier matrices and nonuniform fast Fourier transforms.
SIAM J. Sci. Comput., 21:283 - 293, 1999.

41

A. Nieslony and G. Steidl.
Approximate factorizations of Fourier matrices with nonequispaced knots.
Linear Algebra Appl., 266:337 - 351, 2003.

42

J. Pelt.
Fast computation of trigonometric sums with applications to frequency analysis of astronomical data.
In D. Maoz, A. Sternberg, and E. Leibowitz, editors, Astronomical Time Series, pages 179 - 182, Kluwer, 1997.

43

G. Pöplau, D. Potts, and U. van Rienen.
Calculation of 3d space-charge fields of bunches of charged particles by fast summation.
In Proceedings of SCEE 2004 (5th International Workshop on Scientific Computing in Electrical Engineering, 2005.

44

D. Potts.
Fast algorithms for discrete polynomial transforms on arbitrary grids.
Linear Algebra Appl., 366:353 - 370, 2003.

45

D. Potts.
Schnelle Fourier-Transformationen für nichtäquidistante Daten und Anwendungen.
Habilitation, Universität zu Lübeck, 2003.

46

D. Potts and G. Steidl.
New Fourier reconstruction algorithms for computerized tomography.
In A. Aldroubi, A. Laine, and M. Unser, editors, Proceedings of SPIE: Wavelet Applications in Signal and Image Processing VIII, volume 4119, pages 13 - 23, 2000.

47

D. Potts and G. Steidl.
A new linogram algorithm for computerized tomography.
IMA J. Numer. Anal., 21:769 - 782, 2001.

48

D. Potts and G. Steidl.
Fourier reconstruction of functions from their nonstandard sampled Radon transform.
J. Fourier Anal. Appl., 8:513 - 533, 2002.

49

D. Potts and G. Steidl.
Fast summation at nonequispaced knots by NFFTs.
SIAM J. Sci. Comput., 24:2013 - 2037, 2003.

50

D. Potts, G. Steidl, and A. Nieslony.
Fast convolution with radial kernels at nonequispaced knots.
Numer. Math., 98:329 - 351, 2004.

51

D. Potts, G. Steidl, and M. Tasche.
Fast algorithms for discrete polynomial transforms.
Math. Comput., 67:1577 - 1590, 1998.

52

D. Potts, G. Steidl, and M. Tasche.
Fast Fourier transforms for nonequispaced data: A tutorial.
In J. J. Benedetto and P. J. S. G. Ferreira, editors, Modern Sampling Theory: Mathematics and Applications, pages 247 - 270. Birkhäuser, Boston, 2001.

53

R. A. Scramek and F. R. Schwab.
Imaging.
In R. Perley, F. R. Schwab, and A. Bridle, editors, Astronomical Society of the Pacific Conference, volume 6, pages 117 - 138, 1988.

54

F. Sprengel.
A class of function spaces and interpolation on sparse grids.
Numer. Funct. Anal. Optim., 21:273 - 293, 2000.

55

G. Steidl.
A note on fast Fourier transforms for nonequispaced grids.
Adv. Comput. Math., 9:337 - 353, 1998.

56

B. Tian and Q. H. Liu.
Nonuniform fast cosine transform and Chebyshev PSTD algorithm.
J. Electromagnet. Waves Appl, 14:797 - 798, 2000.

57

A. F. Ware.
Fast approximate Fourier transforms for irregularly spaced data.
SIAM Rev., 40:838 - 856, 1998.

58

C. Zenger.
Sparse grids.
In Parallel algorithms for partial differential equations (Kiel, 1990), volume 31 of Notes Numer. Fluid Mech., pages 241-251. Vieweg, Braunschweig, 1991.