volume | PIER Journals

Abstract

This paper presents a fast and effective electromagnetic reconstruction algorithm with phaseless data under weak scattering conditions. The proposed algorithm is based on the phaseless data multiplicative regularized contrast sources inversion method (PD-MRCSI). We recast the weak scattering problem as an optimization problem in terms of the undetermined contrast and contrast sources. Using the conjugate gradient iterative method, the problem is solved by alternately updating the contrast sources and the contrast. Additionally, this method can combine with the PD-MRCSI method. Taking advantage of the properties of fast convergence of this algorithm and stable convergence of PD-MRCSI method, the combined technique makes image reconstructions more fast and effective. Although the method is derived from weak scattering situation, it is also useful for the case which weak scattering approximation is not satisfied. The synthetic numerical reconstruction results, as well as experimental reconstruction results, presented that the proposed method is a very fast and effective reconstruction algorithm.

1. Chew, W. C. and Y. M. Wang, "Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method," IEEE Trans. Med. Imaging., Vol. 9, 218-225, 1990.
doi:10.1109/42.56334 Google Scholar

2. Zhang, Z. Q. and Q. H. Liu, "Two nonlinear inverse methods for electromagnetic induction measurements," IEEE Trans. Geosci. Remote Sens., Vol. 39, 1331-1339, 2001.
doi:10.1109/36.927456 Google Scholar

3. Van den Berg, P. M. and R. E. Kleinman, "A contrast source inversion method," Inverse Problems, Vol. 13, 1607-1620, 1997.
doi:10.1088/0266-5611/13/6/013 Google Scholar

4. Abubakar, A., T. M. Habashy, and P. M. van den Berg, "Nonlinear inversion of multi-frequency microwave Fresnel data using the multiplicative regularized contrast source inversion," Progress In Electromagnetics Research, Vol. 62, 193-201, 2006.
doi:10.2528/PIER06042205 Google Scholar

5. Abubakar, A., P. M. van den Berg, and S. Y. Semenov, "A robust iterative method for born inversion," IEEE Trans. Geosci. Remote Sens., Vol. 42, 342-354, 2004.
doi:10.1109/TGRS.2003.821062 Google Scholar

6. Abubakar, A., P. M. van den Berg, and S. Y. Semenov, "Two- and three-dimensional algorithms for microwave imaging and inverse scattering ," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 2, 209-231, 2003.
doi:10.1163/156939303322235798 Google Scholar

7. Crocco, L. and T. Isernia, "Inverse scattering with real data: Detecting and imaging homogeneous dielectric objects," Inverse Problems, Vol. 17, 1573-1583, 2001.
doi:10.1088/0266-5611/17/6/302 Google Scholar

8. Torresverdin, C. and T. M. Habashy, "Rapid 2.5-dimensional forward modeling and inversion via a new nonlinear scattering approximation," Radio Sci., Vol. 29, 1051-1079, 1994.
doi:10.1029/94RS00974 Google Scholar

9. Zhdanov, M. and G. Hursan, "3D electromagnetic inversion based on quasi-analytical approximation," Inverse Problems, Vol. 16, 1297-1322, 2000.
doi:10.1088/0266-5611/16/5/311 Google Scholar

10. Guo, B., Y. Wang, J. Li, P. Stoica, and R. Wu, "Microwave imaging via adaptive beamforming methods for breast cancer detection," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 1, 53-63, 2006.
doi:10.1163/156939306775777350 Google Scholar

11. Karanasiou, I. S., N. K. Uzunoglu, and A. Garetsos, "Electro-magnetic analysis of a non-invasive 3D passive microwave imaging system," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 3, 379-380, 2004.
doi:10.1163/156939304323085793 Google Scholar

12. Franceschini, G., M. Donelli, D. Franceschini, M. Benedetti, P. Rocca, and A. Massa, "Microwave imaging from amplitude-only data-advantages and open problems of a two-step multi-resolution strategy ," Progress In Electromagnetics Research, Vol. 83, 397-412, 2008.
doi:10.2528/PIER08062904 Google Scholar

13. Zhou, H., T. Takenaka, J. Johnson, and T. Tanaka, "A breast imaging model using microwaves and a time domain three dimensional reconstruction method," Progress In Electromagnetics Research, Vol. 93, 57-70, 2009.
doi:10.2528/PIER09033001 Google Scholar

14. Dai, S. Y., C. Zhang, and Z.-S. Wu, "Electromagnetic scattering of objects above ground using MRTD/FDTD hybrid method," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 16, 2187-2196, 2006.
doi:10.1163/156939309790109306 Google Scholar

15. Caorsi, S., A. Massa, M. Pastorino, and A. Randazzo, "Electromagnetic detection of dielectric scatterers using phaseless synthetic and real data and the memetic algorithm," IEEE Trans. Geosci. Remote Sens., Vol. 41, 2745-2753, 2003.
doi:10.1109/TGRS.2003.815676 Google Scholar

16. Litman, A. and K. Belkebir, "Two-dimensional inverse profiling problem using phaseless data," J. Opt. Soc. Am. A, Vol. 23, 2737-2746, 2006.
doi:10.1364/JOSAA.23.002737 Google Scholar

17. Crocco, L., M. D'Urso, and T. Isernia, "Faithful non-linear imaging from only-amplitude measurements of incident and total fields," Optics Express, Vol. 15, 3804-3815, 2007.
doi:10.1364/OE.15.003804 Google Scholar

18. D'Urso, M., K. Belkebir, L. Crocco, T. Isernia, and A. Litman, "Phaseless imaging with experimental data: Facts and challenges," J. Opt. Soc. Am. A, Vol. 25, 271-281, 2008.
doi:10.1364/JOSAA.25.000271 Google Scholar

19. Zheng, H., L. Li, and F. Li, "A multi-frequency MRCSI algorithm with phaseless data," Inverse Problems, Vol. 25, 1-13, 2009. Google Scholar

20. Li, L. L., H. Zheng, and F. Li, "Two-dimensional contrast source inversion method with phaseless data: TM case," IEEE Trans. Geosci. Remote Sens., Vol. 47, 1719-1736, 2009.
doi:10.1109/TGRS.2008.2006360 Google Scholar

21. Belkebir, K. and M. Saillard, "Special section: Test inversion algorithms against experimental data," Inverse Problems, Vol. 17, 1565-1571, 2001.
doi:10.1088/0266-5611/17/6/301 Google Scholar

Dr. Hu Zheng

Dr. Ming-Zhen Wang

Professor Zhiqin Zhao

Prof. Lianlin Li