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2025-07-05
A Microwave Imaging Solution to Inverse Scattering Problem Using Distorted Born Iterative Method with Hybrid LSQR
By
Progress In Electromagnetics Research B, Vol. 112, 105-112, 2025
Abstract
DBIM is a deterministic iterative method which exhibits second-order convergence indicating that the reconstruction error decreases quadratically with successive iterations. Existing regularization techniques when applied with DBIM often face challenges in determining the optimal regularization parameter (λ), leading to inconsistent convergence across various problems. To address this, a quantitative imaging algorithm is proposed in this paper by combining the Distorted Born Iterative Method (DBIM) and Hybrid LSQR method for solving Inverse Scattering Problems (ISP). This enhances the accuracy of the reconstructed object profiles and optimizes the regularization level to prevent both under- and over-regularization. For a fair comparison with the results in the literature, simulation studies are conducted using a breast profile that has two tumor inclusions, each with a radius of 6 mm, and two fibro-glandular tissue inclusions, each with a radius of 10 mm. The proposed method achieves a Root Mean Square Error (RMSE) of 0.75, indicating a better level of accuracy. The experimental validation is performed using a phantom made of Delrin material. The Delrin phantom, with a diameter of 10 cm, contains three inclusions made of PVC material with diameters of 10 mm, 6 mm and 3 mm. These inclusions have been successfully reconstructed with errors 0.085, 0.128 and 0.165 respectively. These results demonstrate the effectiveness of this algorithm in reconstructing both high and low-dielectric profiles, making it suitable for microwave imaging applications.
Citation
Soumya Nharakkat, Thathamkulam Anjit, Anju Maria, and Palayyan Mythili, "A Microwave Imaging Solution to Inverse Scattering Problem Using Distorted Born Iterative Method with Hybrid LSQR," Progress In Electromagnetics Research B, Vol. 112, 105-112, 2025.
doi:10.2528/PIERB25042808
References

1. Dey, Sukomal and Athul O. Asok, "A review on microwave imaging for breast cancer detection," 2024 IEEE Wireless Antenna and Microwave Symposium (WAMS), 1-5, Visakhapatnam, India, 2024.

2. Khalid, Nazish, Muhammad Zubair, Muhammad Qasim Mehmood, and Yehia Massoud, "Emerging paradigms in microwave imaging technology for biomedical applications: Unleashing the power of artificial intelligence," Npj Imaging, Vol. 2, No. 1, 13, 2024.

3. Mikhnev, V. and P. Vainikainen, "Microwave imaging of layered structures in civil engineering," 2002 32nd European Microwave Conference, 1-4, Milan, Italy, 2002.

4. Feng, Maria Q., Franco De Flaviis, and Yoo Jin Kim, "Use of microwaves for damage detection of fiber reinforced polymer-wrapped concrete structures," Journal of Engineering Mechanics, Vol. 128, No. 2, 172-183, 2002.

5. Lockwood, Stephanie J. and Hua Lee, "Pulse‐echo microwave imaging for NDE of civil structures: Image reconstruction, enhancement, and object recognition," International Journal of Imaging Systems and Technology, Vol. 8, No. 4, 407-412, 1997.

6. Li, Zhen, Constantinos Soutis, Arthur Haigh, Robin Sloan, Andrew Gibson, and Noushin Karimian, "Microwave imaging for delamination detection in T-joints of wind turbine composite blades," 2016 46th European Microwave Conference (EuMC), 1235-1238, London, UK, 2016.

7. Liao, Yuxuan, Zhongyuan Zhou, and Feng Tian, "Microwave imaging system based on synthetic aperture radar algorithm," 2023 IEEE 6th Information Technology,Networking,Electronic and Automation Control Conference (ITNEC), Vol. 6, 281-284, Chongqing, China, 2023.

8. Yashaswini, Patteti, Urvashi Singh, and Jayanta Mukherjee, "Enhancing early-stage breast cancer detection: Antenna design, realistic phantom modeling, and multi-static imaging with DAS algorithm," 2024 11th International Conference on Signal Processing and Integrated Networks (SPIN), 409-414, Noida, India, 2024.

9. Park, Won-Kwang, "Application of MUSIC algorithm in real-world microwave imaging of unknown anomalies from scattering matrix," Mechanical Systems and Signal Processing, Vol. 153, 107501, 2021.

10. Etminan, Aslan and Mahta Moghaddam, "Microwave imaging of dielectric objects using a combination of simulated annealing and multi-directional search," 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting, 2371-2372, San Diego, CA, USA, 2017.

11. Mhamdi, Bouzid, Khaled Grayaa, and Taoufik Aguili, "Microwave imaging of dielectric cylinders from experimental scattering data based on the genetic algorithms, neural networks and a hybrid micro genetic algorithm with conjugate gradient," AEU --- International Journal of Electronics and Communications, Vol. 65, No. 2, 140-147, 2011.

12. Randazzo, Andrea, "Swarm optimization methods in microwave imaging," International Journal of Microwave Science and Technology, Vol. 2012, No. 1, 491713, 2012.

13. Bilgin, Egemen, Semih Doğu, Sema Coşğun, and Mehmet Çayören, "A modified newton method formulation for microwave imaging," 2020 IEEE Asia-Pacific Microwave Conference (APMC), 1057-1059, Hong Kong, Hong Kong, 2020.

14. Nordebo, Sven and Mats Gustafsson, "A priori modeling for gradient based inverse scattering algorithms," Progress In Electromagnetics Research B, Vol. 16, 407-432, 2009.

15. Tajik, Daniel, Aaron D. Pitcher, and Natalia K. Nikolova, "Comparative study of the Rytov and Born approximations in quantitative microwave holography," Progress In Electromagnetics Research B, Vol. 79, 1-19, 2017.

16. Amin, Bilal, Atif Shahzad, Martin O’halloran, Barry Mcdermott, and Adnan Elahi, "Experimental validation of microwave imaging prototype and DBIM-IMATCS algorithm for bone health monitoring," IEEE Access, Vol. 10, 42589-42600, 2022.

17. Diao, Huaian, Hongyu Liu, Qingle Meng, and Li Wang, "Effective medium theory for embedded obstacles in electromagnetic scattering with applications," Journal of Differential Equations, Vol. 437, 113283, 2025.

18. Vargas, Jose O. and Ricardo Adriano, "Subspace-based conjugate-gradient method for solving inverse scattering problems," IEEE Transactions on Antennas and Propagation, Vol. 70, No. 12, 12139-12146, 2022.

19. Ireland, David, Konstanty Bialkowski, and Amin Abbosh, "Microwave imaging for brain stroke detection using Born iterative method," IET Microwaves, Antennas & Propagation, Vol. 7, No. 11, 909-915, 2013.

20. Mousavi, Sayyed Saleh Sayyed and Mohammad Saeed Majedi, "A quantitative microwave imaging approach for brain stroke classification based on the generalized tikhonov regularization," IEEE Access, Vol. 11, 73370-73376, 2023.

21. Yaswanth, K. and Uday K. Khankhoje, "Two-dimensional non-linear microwave imaging with total variation regularization," 2017 Progress in Electromagnetics Research Symposium --- Fall (PIERS --- FALL), 1509-1513, Singapore, 2017.

22. Khajehnejad, M. Amin, Weiyu Xu, A. Salman Avestimehr, and Babak Hassibi, "Weighted ℓ 1 minimization for sparse recovery with prior information," 2009 IEEE International Symposium on Information Theory, 483-487, Seoul, Korea (South), 2009.

23. Shah, Pratik, Uday K. Khankhoje, and Mahta Moghaddam, "Inverse scattering using a joint L1-L2 norm-based regularization," IEEE Transactions on Antennas and Propagation, Vol. 64, No. 4, 1373-1384, 2016.

24. Bayram, İlker, "On the convergence of the iterative shrinkage/thresholding algorithm with a weakly convex penalty," IEEE Transactions on Signal Processing, Vol. 64, No. 6, 1597-1608, 2016.

25. Beck, Amir and Marc Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM Journal on Imaging Sciences, Vol. 2, No. 1, 183-202, 2009.

26. Benny, Ria, Thathamkulam A. Anjit, Philip Cherian, and Palayyan Mythili, "A combinatorial approach to quantitative microwave imaging for breast tumour profiling using SVBIM and SpaRSA," Progress In Electromagnetics Research C, Vol. 139, 45-57, 2024.

27. Al-Mahdawi, Hassan K. Ibrahim, Hussein Alkattan, Mostafa Abotaleb, Ammar Kadi, and El-Sayed M. El-kenawy, "Updating the landweber iteration method for solving inverse problems," Mathematics, Vol. 10, No. 15, 2798, 2022.

28. Cui, Tie Jun, Weng Cho Chew, Alaeddin A. Aydiner, and Siyuan Chen, "Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using the distorted Born iterative method," IEEE Transactions on Geoscience and Remote Sensing, Vol. 39, No. 2, 339-346, 2001.

29. Huang, Yi and ZhongXiao Jia, "Some results on the regularization of LSQR for large-scale discrete ill-posed problems," Science China Mathematics, Vol. 60, 701-718, 2017.

30. Gazzola, Silvia and Paolo Novati, "Automatic parameter setting for Arnoldi-Tikhonov methods," Journal of Computational and Applied Mathematics, Vol. 256, 180-195, 2014.

31. Gazzola, Silvia, Per Christian Hansen, and James G. Nagy, "IR Tools: A MATLAB package of iterative regularization methods and large-scale test problems," Numerical Algorithms, Vol. 81, No. 3, 773-811, 2019.

32. Chung, Julianne, James G. Nagy, Dianne P. O’leary, et al. "A weighted GCV method for Lanczos hybrid regularization," Electronic Transactions on Numerical Analysis, Vol. 28, No. 149-167, 2008, 2008.

33. Yaswanth, K., Sayak Bhattacharya, and Uday K. Khankhoje, "Algebraic reconstruction techniques for inverse imaging," 2016 International Conference on Electromagnetics in Advanced Applications (ICEAA), 756-759, Cairns, QLD, Australia, 2016.

34. Havelková, Eva and Iveta Hnětynková, "Residual norm behavior for Hybrid LSQR regularization," Programs and Algorithms of Numerical Mathematics, 65-74, 2023.

35. Anjit, Thathamkulam, Ria Benny, Philip Cherian, and Mythili Palayyan, "Microwave imaging solutions for medical imaging using re-weighted basic pursuit algorithm," Progress In Electromagnetics Research M, Vol. 97, 13-24, 2020.

36. 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 Ap plied Electromagnetics (ANTEM), 2006.

37. 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 (Cat. No.02CH37278), Vol. 3, 1759-1762, Seattle, WA, USA, 2002.

38. Jamali, Nor Haizan, K. A. Hong Ping, Shafrida Sahrani, and T. Takenaka, "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.

39. Cherian, Philip, T. A. Anjit, and P. Mythili, "A compact egg-shaped UWB antenna for breast dielectric profile imaging," International Journal of Scientific & Technology Research, Vol. 9, No. 03, 4672-4681, 2020.