Vol. 58
Latest Volume
All Volumes
PIERB 105 [2024] PIERB 104 [2024] PIERB 103 [2023] PIERB 102 [2023] PIERB 101 [2023] PIERB 100 [2023] PIERB 99 [2023] PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2014-01-06
Dyadic Point Spread Functions for 3D Inverse Source Imaging Based on Analytical Integral Solutions
By
Progress In Electromagnetics Research B, Vol. 58, 1-17, 2014
Abstract
Imaging is a valuable tool for solving inverse source problems. The achievable image quality is determined by the imaging system. Its performance can be evaluated by using the concept of point spread functions (PSFs). It is common to compute the PSFs using a numerical algorithm. However, in some cases the PSFs can be derived analytically. In this work, new analytical PSFs are presented. The results apply to scalar and dyadic scenarios in 3D originating from acoustics and electromagnetics. Data sets with narrow angular acquisition or complete spherical coverage are considered, where broadband and narrowband frequency domain data is supported. Several visualizations accompany the resulting formulas. Finally, the analytical PSFs are verified using a numerical implementation of the imaging process.
Citation
Georg Schnattinger, and Thomas F. Eibert, "Dyadic Point Spread Functions for 3D Inverse Source Imaging Based on Analytical Integral Solutions," Progress In Electromagnetics Research B, Vol. 58, 1-17, 2014.
doi:10.2528/PIERB13111503
References

1. Sarty, G. E., R. Bennet, and R. W. Cox, Direct reconstruction of non-Cartesian k-space data using a nonuniform fast Fourier transform, Vol. 45, 908-915, Magnetic Resonance in Medicine, 2001.

2. Basu, S. and Y. Bresler, "An O(N2 log2 N) filtered back-projection reconstruction algorithm for tomography," IEEE Trans. on Image Process., Vol. 9, No. 10, 1760-1773, Oct. 2000.
doi:10.1109/83.869187

3. Boag, A., "A fast multilevel domain decomposition algorithm for radar imaging," IEEE Trans. on Antennas and Propag., Vol. 49, No. 4, 666-671, Apr. 2001.
doi:10.1109/8.923329

4. Schnattinger, G., C. Schmidt, and T. Eibert, "3-D imaging by hierarchical disaggregation," German Microwave Conference (GeMiC), 1-4, Mar. 2011.

5. Desai, M. D. and W. K. Jenkins, "Convolution backprojection image reconstruction for spotlight mode synthetic aperture radar," IEEE Trans. on Image Process., Vol. 4, No. 4, 505-517, 1992.
doi:10.1109/83.199920

6. Mensa, D. L., "High Resolution Radar Cross-section Imaging," Artech House Inc., 1990.

7. Majumder, U. K., M. A. Temple, M. J. Minardi, and E. G. Zelnio, "Point spread function characterization of a radially displaced scatterer using circular synthetic aperture radar," IEEE Radar Conference, 729-733, Apr. 2007.

8. Maussang, F., F. Daout, G. Ginolhac, and F. Schmitt, "GPS ISAR passive system characterization using point spread function," New Trends for Environmental Monitoring Using Passive Systems, 1-4, Oct. 2008.
doi:10.1109/PASSIVE.2008.4786989

9. Tathee, S., Z. J. Koles, and T. R. Overton, "Image restoration in computed tomography: Estimation of the spatially variant point spread function," IEEE Trans. on Med. Imag., Vol. 11, No. 4, 539-545, Dec. 1992.
doi:10.1109/42.192689

10. Gallatin, G. M., "Analytic evaluation of the intensity point spread function," Journal of Vaccum Science and Technology B, Vol. 18, No. 6, 3023-3028, Nov. 2000.
doi:10.1116/1.1324617

11. Berizzi, F., E. Mese, M. Diani, and M. Martorella, "High-resolution ISAR imaging of maneuvering targets by means of the range instantaneous Doppler technique: Modeling and performance analysis ," IEEE Trans. on Image Process., Vol. 10, No. 12, 1890-1890, Dec. 2001.
doi:10.1109/83.974573

12. Buddendick, H. and T. F. Eibert, "Bistatic image formation from shooting and bouncing rays simulated current distributions," Progress In Electromagnetics Research, Vol. 119, 1-18, 2011.
doi:10.2528/PIER11060212

13. Schnattinger, G. and T. F. Eibert, "Solution to the full vectorial 3D inverse source problem by multi-level fast multipole method inspired hierarchical disaggregation," IEEE Trans. on Antennas and Propag., Vol. 60, No. 7, 3325-3335, Jul. 2012.
doi:10.1109/TAP.2012.2196946

14. Schnattinger, G., C. H. Schmidt, and T. F. Eibert, "Analysis of 3-D images generated by hierarchical disaggregation," Proc. Int. Radar Symp. (IRS), 365-370, Sep. 2011.

15. Rade, L. and B. Westergren, Mathematics Handbook for Science and Engineering, 5th Ed., Springer, 2004.
doi:10.1007/978-3-662-08549-3_15

16. Rosenthal, A., D. Razansky, and V. Ntziachristos, "Fast semi-analytical model-based acoustic inversion for quantitative optoacoustic tomography," IEEE Trans. on Image Process., Vol. 29, No. 6, 1275-1285, 2010.

17. Balanis, C., "Advanced Engineering Electromagnetics," ser. CourseSmart Series, Wiley, 2012.
doi:http://books.google.de/books?id=cRkTuQAACAAJ

18. Stratton, J. A., Electromagnetic Theory, El-Hawar Ed., IEEE Press, 2007.

19. Woods, J. W., Multidimensional Signal, Image, and Video Processing and Coding, Academic Press, 2011.

20. SciFace Software MuPAD (Multi Processing Algebra Data Tool), SciFace Software, Paderborn, Germany, 2012.
doi:www.mupad.de

21. The MathWorks Inc. "MATLAB (Matrix Laboratory)," The MathWorks Inc., 2012.
doi:www.mathworks.com