volume | PIER Journals

Abstract

This paper describes an innovative technique for the quantitative reconstruction of the dielectric and conductivity distribution of objects in a microwave tomography framework using sparse data. The proposed method tries to extract information about the size, shape, localisation and dielectric distribution of various inclusions within the object under study using an iterative reconstruction methodology in the sparse domain. The proposed algorithm combines the Distorted Born Iteration method (DBIM) and a convex optimization technique for solving the inverse ill-posed problem. The Re-weighted Basis Pursuit (RwBP) algorithm is chosen as the convex optimization technique in this work. The performance of the proposed algorithm has been compared with the TV-norm method, and the results obtained are highly encouraging. The proposed method produces a significant reduction in the reconstruction error as compared to the TV norm method with an error value of 0.083 as against 0.32 in the case of TV norm in the presence of 25 dB noise. By accurately preserving the edges of the inclusions the proposed technique is found to provide an overall improvement in the reconstruction in terms of tissue differentiation (permittivity and conductivity), dimensions of inclusions, resolution, shape, size and coordinate localisation of inclusions. The proposed algorithm converges within 10-12 iterations as compared to other complex imaging algorithms available in the literature. Further, this proposed technique is validated using experimental data from an actual breast imaging setup. The three inclusions of 10 mm, 6 mm, and 3 mm have been localised with errors of 0.052, 0.04, and 0.09, respectively The results obtained from the real-time data show the applicability and feasibility of the proposed algorithm in breast tumor imaging application

1. Semenov, S. Y., A. E. Bulyshev, V. G. Posukh, Y. E. Sizov, T. C. Williams, and A. E. Souvorov, "Microwave tomography for detection/imaging of myocardial infarction. 1. Excised canine hearts," Ann. Biomed. Eng., Vol. 31, 262-270, 2003.
doi:10.1114/1.1553452 Google Scholar

2. Anishchenko, L. N., I. L. Alborova, M. A. Chizh, and A. V. Zhuravlev, "Microwave imaging of biological tissue phantom in different frequency ranges," 2016 Progress In Electromagnetic Research Symposium (PIERS), 4639-4643, Shanghai, China, August 8–11, 2016. Google Scholar

3. Yaswanth, K., S. Bhattacharya, and U. K. Khankhoje, "Algebraic reconstruction techniques for inverse imaging," 2016 International Conference on Electromagnetics in Advanced Applications (ICEAA), Cairns, Australia, September 2016. Google Scholar

4. Benny, R., T. A. Anjit, and P. Mythili, "An overview of microwave imaging for breast tumor detection," Progress In Electromagnetics Research B, Vol. 87, 61-91, 2020.
doi:10.2528/PIERB20012402 Google Scholar

5. Huang, T. and A. S. Mohan, "Microwave imaging of perfect electrically conducting cylinder by micro-genetic algorithm," IEEE Antennas and Propagation Society Symposium, Vol. 1, IEEE, 2004. Google Scholar

6. Semenov, S. Y., et al., "Microwave-tomographic imaging of the high dielectric-contrast objects using different image-reconstruction approaches," IEEE Trans. Microw. Theory Tech., Vol. 53, No. 7, 2284-2294, July 2005.
doi:10.1109/TMTT.2005.850459 Google Scholar

7. Chew, W. C. and G. P. Otto, "Microwave imaging of multiple metallic cylinders using shape functions," IEEE Antennas and Propagation Society International Symposium, 1992 Digest, IEEE, 1992. Google Scholar

8. Colgan, T. J., S. C. Hagness, and B. D. van Veen, "A 3-D level set method for microwave breast imaging," IEEE Trans. Biomed. Eng., Vol. 62, No. 10, 2526-2534, 2015.
doi:10.1109/TBME.2015.2435735 Google Scholar

9. Bayat, N. and P. Mojabi, "A mathematical framework to analyze the achievable resolution from microwave tomography," IEEE Trans. Antennas and Propag., Vol. 64, No. 4, 1484-1489, 2016.
doi:10.1109/TAP.2016.2526061 Google Scholar

10. Rocca, P., M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, "Evolutionary optimization as applied to inverse problems," Inverse Prob., Vol. 25, 1-41, 2009. Google Scholar

11. Majobi, P. and J. LeVetri, "Comparison of TE and TM inversions in the framework of the GaussNewton method," IEEE Trans. Antennas and Propag., Vol. 64, 1336-1348, 2010.
doi:10.1109/TAP.2010.2041156 Google Scholar

12. Candes, E. J. and M. B. Wakin, "An introduction to compressive sampling," IEEE Signal Processing Magazine, Vol. 25, No. 2, 21-30, 2008.
doi:10.1109/MSP.2007.914731 Google Scholar

13. Lustig, M., D. Donoho, and J. M. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magnetic Resonance in Medicine, Vol. 58, No. 6, 1182-1195, 2008.
doi:10.1002/mrm.21391 Google Scholar

14. Pan, X. and E. Y. Sidky, "Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization," Physics in Medicine and Biology, Vol. 53, No. 17, 4777-4807, 2008.
doi:10.1088/0031-9155/53/17/021 Google Scholar

15. Chinn, G., P. D. Olcott, and C. S. Levin, "Sparse signal recovery methods for multiplexing PET detector readout," IEEE Transactions on Medical Imaging, Vol. 32, 932-942, 2013.
doi:10.1109/TMI.2013.2246182 Google Scholar

16. Rudin, L. I. and S. Osher, "Total variation based image restoration with free local constraints," Proc. International Conf. Image Processing, Austin, USA, 1994. Google Scholar

17. Zhou, H. and R. M. Narayan, "Microwave imaging of nonsparse object using dual-mesh method and iterative method," IEEE Trans. Antennas and Propag., Vol. 67, 504-512, 2019.
doi:10.1109/TAP.2018.2876164 Google Scholar

18. Yalcin, E. and O. Ozdemir, "Sparsity based regularization for microwave imaging with NESTA algorithm," Proc. IEEE Conference on Antennas Measurements and Applications (CAMA), Tsukuba, Japan, 2017. Google Scholar

19. Jamali, N. H., et al., "Image reconstruction based on combination of inverse scattering technique and total variation regularization method," Indonesian Journal of Electrical Engineering and Computer Science, Vol. 5, No. 3, 569-576, 2017.
doi:10.11591/ijeecs.v5.i3.pp569-576 Google Scholar

20. Chen, S. and D. Donoho, "Basis pursuit,", Technical Report, Department of Statistics, Stanford University, 1995. Google Scholar

21. Azghani, M. and F. Marvasti, "L2-regularized iterative weighted algorithm for inverse scattering," IEEE Trans. Antennas and Propag., Vol. 64, No. 6, 2293-2300, 2016.
doi:10.1109/TAP.2016.2546385 Google Scholar

22. Tibshirani, R., "Regression shrinkage and selection via the LASSO," J. Roy. Statist. Soc., ser. B, Vol. 58, No. 1, 267-288, 1996. Google Scholar

23. Chartrand, R. and V. Staneva, "Restricted isometry properties and nonconvex compressive sensing," Inverse Prob., Vol. 24, 035020, 2008.
doi:10.1088/0266-5611/24/3/035020 Google Scholar

24. Wang, Y., J. Zeng, Z. Peng, X. Chang, and Z. Xu, "Linear convergence of adaptively iterative thresholding algorithms for compressed sensing," IEEE Transactions on Signal Processing, Vol. 63, No. 11, 2957-2971, June 2015.
doi:10.1109/TSP.2015.2412915 Google Scholar

25. Mansour, H. and O. Yilmaz, "Support driven reweighted 1 minimization," 2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012. Google Scholar

26. Asif, M. S. and J. Romberg, "Sparse recovery of streaming signals using l₁-homotopy," IEEE Transactions on Signal Processing, Vol. 62, No. 16, 4209-4223, July 2014.
doi:10.1109/TSP.2014.2328981 Google Scholar

27. Tavassolian, N., H. Kanj, and M. Popovic, "Assessment of Dark eyes antenna radiation in the vicinity of the realistic breast model," 12th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM), Montreal, Canada, July 2006. Google Scholar

28. Fear, E. C. and M. Okoniewski, "Confocal microwave imaging for breast tumor detection: Application to a hemispherical breast model," 2002 IEEE MTT-S International Microwave Symposium Digest, Vol. 3, 1759-1762, June 2–7, 2002. Google Scholar

29. Estatico, C., M. Pastorino, and A. Randazzo, "A novel microwave imaging approach based on regularization in banach spaces," IEEE Trans. Antennas and Propag., Vol. 60, No. 7, 3373-3381, 2012.
doi:10.1109/TAP.2012.2196925 Google Scholar

30. Fear, E. C., X. Li, S. C. Hagness, and M. A. Stuchly, "Confocal microwave imaging for breast cancer detection: Localization of tumors in three dimensions," IEEE Trans. Biomed. Eng., Vol. 49, No. 8, 812-822, 2002.
doi:10.1109/TBME.2002.800759 Google Scholar

31. Philip, C., T. A. Anjit, and P. Mythili, "A compact egg-shaped UWB antenna for breast dielectric profile imaging," International Journal of Scientific & Technology Research (IJSTR), Vol. 9, No. 3, March 2020. Google Scholar

Dr. Thathamkulam Agamanandan Anjit

Ms. Ria Benny

Dr. Philip Cherian

Dr. Mythili Palayyan