Vol. 142
Latest Volume
All Volumes
PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2013-10-16
Parameter Selection and Accuracy in Type-3 Non-Uniform FFTs Based on Gaussian Gridding
By
Progress In Electromagnetics Research, Vol. 142, 743-770, 2013
Abstract
We provide a sucient condition to select the parameters of Type 3 Non-Uniform Fast Fourier Transform (NUFFT) algorithms based on the Gaussian gridding to ful ll a prescribed accuracy. This is a problem of signi cant interest in many areas of applied electromagnetics, as for example fast antenna analysis and synthesis and fast calculation of the scattered elds, as well as in medical imaging comprising ultrasound tomography, computed axial tomography, positron emission tomogr aphy and magnetic resonance imaging. The approach is related to the one dimensional case and follows the work in A. Dutt and V. Rokhlin, SIAM J. Sci. Comp. 14 (1993). The accuracy of the proposed choice is rst numerically assessed and then compared to that achieved by the approach in J.-Y. Lee and L. Greengard, J. Comp. Phys. 206 (2005). The convenience of the strategy devised in this paper is shown. Finally, the use of the Type 3 NUFFT is highlighted for an electromagnetic application consisting of the implementation of the aggregation and disaggregation steps in the fast calculation of the scattered eld by the Fast Multipole Method.
Citation
Amedeo Capozzoli, Claudio Curcio, Angelo Liseno, and Antonio Riccardi, "Parameter Selection and Accuracy in Type-3 Non-Uniform FFTs Based on Gaussian Gridding," Progress In Electromagnetics Research, Vol. 142, 743-770, 2013.
doi:10.2528/PIER13072402
References

1. Bronstein, M., A. Bronstein, and M. Zibulevsky, "The non-uniform FFT and its applications," , Technical Report of the Vision and Image Science Laboratory, Israel Institute of Technology, Technion, 2002.

2. Lee, J.-Y. and L. Greengard, "The type 3 nonuniform FFT and its applications," J. Comput. Phys., Vol. 206, No. 1, 1-5, Jun. 2005.

3. Capozzoli, A., C. Curcio, and A. Liseno, "GPU-based ω-k tomographic processing by 1D non-uniform FFTs," Progress In Electromagnetics Research M, Vol. 23, 279-298, 2012.

4. Liu, Q. H., X. M. Xu, B. Tian, and Z. Q. Zhang, "Applications of nonuniform fast transform algorithms in numerical solutions of differential and integral equations," IEEE Trans. Geosci. Remote Sens., Vol. 38, No. 4, 1551-1560, Jul. 2000.

5. Li, J.-R., D. Calhoun, and L. Brush, "EffIcient thermal FIeld computation in phase-field models," J. Comput. Phys., Vol. 228, No. 24, 8945-8957, Dec. 2009.

6. Bakir, O., H. Bagci, and E. Michielssen, "Adaptive integral method with fast Gaussian gridding for solving combined field integral equations," Waves Random Media, Vol. 19, No. 1, 147-161, Feb. 2009.

7. Capozzoli, A., C. Curcio, and A. Liseno, "2D fast multipole method (FMM) via type-3 non-uniform FFTs (NUFFTs)," Proc. of the Loughborough Conf. on Antennas Prop., 1-4, Loughborough, UK, Nov. 12-13, 2012.

8. Capozzoli, A., C. Curcio, G. D'Elia, A. Liseno, and P. Vinetti, "Fast CPU/GPU pattern evaluation of irregular arrays," Applied Comput. Electromagn. Soc. J., Vol. 25, No. 4, 355-372, Apr. 2010.

9. Capozzoli, A., C. Curcio, A. Liseno, and G. Toso, "Phase-only synthesis of flat aperiodic reflectarrays," Progress In Electromagnetics Research, Vol. 133, 53-89, 2013.

10. Capozzoli, A., C. Curcio, and A. Liseno, "NUFFT-accelerated plane-polar (also phaseless) near-field/far-field transformation," Progress In Electromagnetics Research M, Vol. 27, 59-73, 2012.

11. Bronstein, M. M., A. M. Bronstein, M. Zibulevsky, and H. Azhari, "Reconstruction in diffraction ultrasound tomography using nonuniform FFT," IEEE Trans. Medical Imaging, Vol. 21, No. 11, 1395-1401, Nov. 2002.

12. Zhang-O'Connor, Y. and J. A. Fessler, "Fourier-based forward and back-projectors in iterative fan-beam tomographic image reconstruction," IEEE Trans. Medical Imaging, Vol. 25, No. 5, 582-589, May 2006.

13. Matej, S., J. A. Fessler, and I. G. Kazantsev, "Iterative tomographic image reconstruction using Fourier-based forward and back-projectors," IEEE Trans. Medical Imaging, Vol. 23, No. 4, 401-412, Apr. 2004.

14. Eggers, H., T. Knopp, and D. Potts, "Field inhomogeneity correction based on gridding reconstruction for magnetic resonance imaging," IEEE Trans. Medical Imaging, Vol. 26, No. 3, 374-384, Mar. 2007.

15. Dutt, A. and V. Rokhlin, "Fast Fourier transforms for nonequispaced data," SIAM J. Sci. Comp., Vol. 14, No. 6, 1368-1393, 1993.

16. Potts, D., G. Steidl, and M. Tasche, "Fast Fourier transforms for nonequispaced data: A tutorial," Modern Sampling Theory: Mathematics and Application, 253-274, J. J. B. P. Ferreira, Ed., Birkhauser, Boston, MA, 2000.

17. Fessler, J. A. and B. P. Sutton, "Nonuniform fast Fourier transforms using min-max interpolation," IEEE Trans. Signal Proc., Vol. 51, No. 2, 560-574, Feb. 2003.

18. Fourmont, K., "Non-equispaced fast Fourier transforms with applications to tomography," J. Fourier Anal. Appl., Vol. 9, No. 5, 431-450, 2003.

19. Greengard, K. and J.-Y. Lee, "Accelerating the nonuniform fast Fourier transform," SIAM Rev., Vol. 46, No. 3, 443-454, 2004.

20. Dutt, A., "Fast Fourier transforms for nonequispaced data," , Ph.D. Dissertation, Yale University, YALEU/CSD/RR #981, 1993.

21. Kantorovich, L. V. and G. P. Akilov, Functional Analysis, Pergamon Press, New York, 1982.

22. Pozrikidis, C., Numerical Computation in Science and Engineering, Oxford University Press, Oxford, 2008.

23. Morita, N., "The boundary-element method," Analysis Methods for Electromagnetic Wave Problems, E. Yamashita (ed.), Artech House, Norwood, MA, 1990.

24. Chew, W. C., J.-M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Norwood, MA, 2001.

25. Song, J. and W. C. Chew, "Error analysis for the truncation of multipole expansion of vector's Green's functions," Microw. Opt. Tech. Lett., Vol. 11, No. 7, 311-313, Jul. 2001.