Quantitative microwave holography is a recent imaging methodology that shows promise in medical diagnostics. It is a real-time direct inversion algorithm that reconstructs the complex permittivity from S-parameter measurements on an acquisition surface outside of the imaged object. It is recognized that this imaging method suers from limitations in tissue imaging due to a forward model which linearizes a highly nonlinear scattering problem. It is therefore important to study its limitations when reconstruction is aided by certain pre- and post-processing filters which are known to improve the image quality. The impact of ltering on the quantitative result is particularly important. In this work, the reconstruction equations of quantitative microwave holography are derived from rst principles. The implementation of two linearizations strategies, Born's approximation and Rytov's approximation, is explained in detail in the case of a scattering model formulated in terms of S-parameters. Furthermore, real-space and Fourier-space lters are developed to achieve the best performance for the given linearized model of scattering. Simulated and experimental results demonstrate the limitations of the method and the necessity of ltering. The two approximations are also compared in experimental tissue reconstructions.
2. Xu, H., T. Li, and Y. Sun, "The application research of microwave imaging in nondestructive testing of concrete wall," Proc. World Cong. Intell. Control Autom., 5157-5161, Dalian, 2006.
3. Kharkovsky, S. and R. Zoughi, "Microwave and millimeter wave nondestructive testing and evaluation — Overview and recent advances," IEEE Instrum. Meas. Mag., Vol. 10, No. 2, 26-38, Apr. 2007.
4. Ahmad, F., M. G. Amin, and S. A. Kassam, "Synthetic aperture beamformer for imaging through a dielectric wall," IEEE Trans. Aerosp. Electron. Syst., Vol. 41, No. 1, 271-283, Jan. 2005.
5. Amin, M. G., Through-the-wall Radar Imaging, CRC Press, 2016.
6. Nikolova, N. K., "Microwave biomedical imaging," Wiley Encyc. Elec. Electron. Eng., 1-22, Apr. 25, 2014.
7. Conceio, R. C., J. J. Mohr, and M. O’Halloran, An Introduction to Microwave Imaging for Breast Cancer Detection, Springer, 2016.
8. Kwon, S. and S. Lee, "Recent advances in microwave imaging for breast cancer detection," Int. J. Biomed. Imaging, Vol. 2016, 25 pages, Article ID 5054912, 2016.
9. Bindu, G. N., S. J. Abraham, A. Lonappan, V. Thomas, C. K. Aanandan, and K. T. Mathew, "Active microwave imaging for breast cancer detection," Progress In Electromagnetics Research, Vol. 58, 149-169, 2006.
10. Porter, E., A. Santorelli, and M. Popovic, "Time-domain microwave radar applied to breast imaging: Measurement reliability in a clinical setting," Progress In Electromagnetics Research, Vol. 149, 119-132, 2014.
11. Wang, X., D. R. Bauer, R. Witte, and H. Xin, "Microwave-induced thermoacoustic imaging model for potential breast cancer detection," IEEE Trans. Biomed. Eng., Vol. 59, No. 10, 2782-2791, Oct. 2012.
12. Xia, J., J. Yao, and L. H. V. Wang, "Photoacoustic tomography: Principles and advances (invited review)," Progress In Electromagnetics Research, Vol. 147, 1-22, 2014.
13. Fear, E. C. and M. A. Stuchly, "Confocal microwave imaging for breast tumor detection: A study of resolution and detection ability," Proc. Int. Conf. IEEE Eng. Med. Bio. Soc., Vol. 3, 2355-2358, 2001.
14. Slaney, M., A. C. Kak, and L. E. Larsen, "Limitations of imaging with first-order diffraction tomography," IEEE Trans. Microw. Theory Techn., Vol. 32, No. 8, 860-874, Aug. 1984.
15. Tu, S., J. J. McCombe, D. S. Shumakov, and N. K. Nikolova, "Fast quantitative microwave imaging with resolvent kernel extracted from measurements," Inverse Probl., Vol. 31, No. 4, 045007 (33 pages), Apr. 2015.
16. Tricoles, G. and N. H. Farhat, "Microwave holography, applications and techniques," Proc. IEEE, Vol. 65, No. 1, 108-121, Jan. 1998.
17. Li, J., X. Wang, and T. Wang, "On the validity of Born approximation," Progress In Electromagnetics Research, Vol. 107, 219-237, 2010.
18. Habashy, T. M., R. W. Groom, and B. R. Spies, "Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering," J. Geophys. Res., Vol. 98, No. B2, 1759-1775, Feb. 1993.
19. Kak, A. and M. Slaney, Principles of Computerized Tomographic Imaging, Society for Industrial and Applied Mathematics, 2001.
20. Chew, W., Waves and Fields in Inhomogeneous Media, IEEE Press, 1995.
21. Nikolova, N. K., Introduction to Microwave Imaging, Cambridge University Press, 2017.
22. Tajik, D., D. S. Shumakov, and N. K. Nikolova, "An experimental comparison between the Born and Rytov approximations in microwave tissue imaging," IEEE Int. Microw. Symp., Jun. 2017.
23. Farhat, N. H. and W. R. Guard, "Millimeter wave holographic imaging of concealed weapons," Proc. IEEE, Vol. 59, No. 9, 1383-1384, Sep. 1971.
24. Amineh, R. K., M. Ravan, J. McCombe, and N. K. Nikolova, "Three-dimensional microwave holographic imaging employing forward-scattered waves only," Int. J. Antennas Propag., Vol. 2013, Article ID 897287 (15 pages), Feb. 2013.
25. Tajik, D., J. R. Thompson, A. S. Beaverstone, and N. K. Nikolova, "Real-time quantitative reconstruction based on microwave holography," IEEE Int. Symp. Antennas Propag. (APS/URSI), 851-852, Fajardo, PR, 2016.
26. Amineh, R. K., J. J. McCombe, A. Khalatpour, and N. K. Nikolova, "Microwave holography using point-spread functions measured with calibration objects," IEEE Trans. Instrum. Meas., Vol. 64, No. 2, 403-417, Feb. 2015.
27. Thompson, J. R., J. J. McCombe, S. Tu, and N. K. Nikolova, "Quantitative imaging of dielectric objects based on holographic reconstruction," 2015 IEEE Radar Conf. (RadarCon), 679-683, May 2015.
28. Khare, K., Fourier Optics and Computational Imaging, Wiley, 2016.
29. Mohamed, S. A., E. D. Mohamed, M. F. Elshikh, and M. A. Hassan, "Design of digital apodization technique for medical ultrasound imaging," Int. Conf. Comput., Electr. Electron. Eng., 541-544, Khartoum, 2013.
30. Bell, R., "Introduction to Fourier transform spectroscopy," Science, 2012.
31. Beaverstone, A. S., D. S. Shumakov, and N. K. Nikolova, "Frequency-domain integral equations of scattering for complex scalar responses," IEEE Trans. Microw. Theory Techn., Vol. 65, No. 4, 1120-1132, Apr. 2016.
32. Pastorino, M., Microwave Imaging, Wiley, 2010.
33. Natterer, F., "An error bound for the Born approximation," Inverse Probl., Vol. 20, No. 2, 447-452, 2004.
34. Slaney, M., A. C. Kak, and L. E. Larsen, "Limitations of imaging with first-order diffraction tomography," IEEE Trans. Microw. Theory Tech., Vol. 32, No. 8, 860-874, 1984.
35. Brown, M. A. and R. C. Semelka, MRI: Basic Principles and Applications, Wiley, 2015.
36. Ansorge, R. and M. Graves, The Physics and Mathematics of MRI, Morgan and Claypool, 2016.
37. Goodman, J. W., Introduction to Fourier Optics, Roberts and Company, 2005.
38. Szabo, T. L., Diagnostic Ultrasound Imaging: Inside and Out, Elsevier, 2014.
39. Jerri, A. J., The Gibbs Phenomenon in Fourier Analysis, Splines, and Wavelet Approximations, Springer-Science Business Media, B. V., New York, 2010.
40. EM Software & Systems — S. A. (Pty) Ltd., FEKO Suite 7.0.1 for Altair, USA, 2016.
41. Keysight (Agilent) Technologies, "Dielectric Probe Kit 200 MHz to 50 GHz, 85070E,", USA, 2014.
42. Shumakov, D. S., A. S. Beaverstone, and N. K. Nikolova, "De-noising algorithm for enhancing microwave imaging," J. Eng., 5 pages, 2017.
43. Amineh, R. K., A. Trehan, and N. K. Nikolova, "TEM horn antenna for ultra-wide band microwave breast imaging," Progress In Electromagnetics Research B, Vol. 13, 59-74, 2009.
44. The MathWorks, Inc., MATLAB 2016a, USA, 2016.