volume | PIER Journals

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.

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, 2012.
doi:www.mupad.de

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

Mr. Georg Schnattinger

Dr. Thomas F. Eibert