This paper proposes a new method to display microwave images of breast tissue, based on estimation of local microwave velocity from time of flight measurements. Its computational demands are low compared with tomography. It has two major components: 1) the estimation of the travel time of microwaves across the tissue between a set of antennae using a wavelet decomposition, and 2) the estimation of the microwave velocity field from the set of travel times using a low dimensional set of radial basis functions to model local velocity. The technique is evaluated in 2-D on clinical MR-based numerical breast phantoms incorporated in Finite-Difference Time-Domain simulations. The basis functions, used with a regularisation scheme to improve numerical stability, reduce the dimensionality of the inverse problem for computational efficiency and also to improve the robustness to error in velocity estimation. The results support previously published findings that the wavelet transform is suitable for robust measurement of time of flight even in clinically significant simulations, and shows that the velocity contrast images can be constructed so different regions of breast tissue type can be distinguished. In particular, the presence of a tumour is clearly detected, demonstrating the potential of this approach for breast screening. Keywords: Biomedical signal processing; Microwave imaging; Image reconstruction.
2. Fletcher, S. W. and J. G. Elmore, "Mammographic screening for breast cancer," New England Journal of Medicine, Vol. 37, 1672-1680, 2003.
3. Nelson, H. D., K. Tyne, A. Naik, C. Bougatsos, B. K. Chan, and L. Humphrey, "Screening for breast cancer: An update for the U.S. preventive services task force ," Annals of Internal Medicine, Vol. 151, No. 10, 716-726, 2009.
4. Meaney, P. M., M. W. Fanning, T. Raynolds, C. J. Fox, Q. Fang, C. A. Kogel, S. P. Poplack, and K. D. Paulsen, "Initial clinical experience with microwave breast imaging in women with normal mammography," Academic Radiology, Vol. 14, 207-218, 2007.
5. Shea, J. D., P. Kosmas, B. D. Van Veen, and S. C. Hagness, "Contrast-enhanced microwave imaging of breast tumours: A computational study using 3-D realistic numerical phantoms," Inverse Problems, Vol. 26, 1-22, 2010.
6. Klemm, M., I. J. Craddock, J. A. Leendertz, A. W. Preece, D. R. Gibbins, M. Shere, and R. Benjamin, "Clinical trials of UWB imaging radar for breast cancer detection," European Conference on Antennas and Propagation (EuCAP), 1-4, Barcelona, Spain, 2010.
7. Gabriel, S., R. W. Lau, and C. Gabriel, "The dielectric properties of biological tissues: II. Measurements on the frequency range 10 Hz to 20 GHz," Phys. Med. Biol., Vol. 41, 2251-2269, 1996.
8. Lazebnik, M., D. Popovic, L. McCartney, C. B. Watkins, M. J. Lindstrom, J. Harter, S. Sewall, T. Ogilvie, A. Magliocco, T. M. Breslin, W. Temple, D. Mew, J. H. Booske, M. Okoniewski, and S. C. Hagness, "A large-scale study of the ultrawideband microwave dielectric properties of normal, benign and malignant breast tissues obtained from cancer surgeries ," Physics in Medicine and Biology, Vol. 52, 6093-6115, 2007.
9. Winters, D. W., J. D. Shea, P. Kosmas, B. D. Van Veen, and S. C. Hagness, "Three-dimensional microwave breast imaging: Dispersive dielectric property estimation using patient-specific basis functions," IEEE Trans. Med. Imaging, Vol. 28, 969-981, 2009.
10. Fang, Q., P. M. Meaney, and K. D. Paulsen, "Viable three-dimensional microwave imaging: Theory and numerical experiments," IEEE Trans. Antennas and Propagation, Vol. 58, 449-458, 2010.
11. Golnabi, A. H., P. M. Meaney, N. R. Epstein, and K. D. Paulsen, "Microwave imaging for breast cancer detection: Advances in three dimensional image reconstruction," Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBC, 5730-5733, Prague, 2011.
12. Li, X., E. J. Bond, B. D. Van Veen, and S. C. Hagness, "An overview of the ultra-wideband microwave imaging via space-time beamforming for early-stage breast-cancer detection," IEEE Antennas and Propagation Magazine, Vol. 47, No. 1, February 2005.
13. Kurrant, D. J., E. C. Fear, and D. T.Westwick, "Tumour response estimation in radar-based microwave breast cancer detection," IEEE Trans. Biomed. Eng., Vol. 55, 2801-2811, 2008.
14. Klemm, M., I. Craddock, J. Leendertz, A. Preece, and R. Benjamin, "Radar-based breast cancer detection using a hemispherical antenna array - Experimental results," IEEE Trans. on Antennas and Propagation, Vol. 57, 1692-1704, 2009.
15. Pourvoyeur, K., A. Stelzer, G. Ossberger, T. Buchegger, and M. Pichler, "Wavelet-based impulse reconstruction in UWB-radar," IEEE Int. Symp. on Microwave Theory and Technology, 603-606, 2003.
16. Lazaro, A., D. G. Firbau, and R. Villarino, "Wavelet based breast tumour localization technique using a UWB radar," Progress In Electromagnetics Research, Vol. 98, 75-95, 2009.
17. Deprez, J.-F., M. Klemm, P. P. Smith, and I. J. Craddock, "Twin target correction for ultra-wideband radar imaging of breast tumours," IEEE International Symposium in Biomedical Imaging, 213-216, 2010.
18. 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, 812-822, 2002.
19. Moody, J. and C. J. Darken, "Fast learning in networks of locally tuned processing units," Neural Computation, Vol. 1, 281-294, 1989.
20. Jovanovic, I., L. Sbaiz, and M. Vitterli, "Acoustic tomography method for measuring temperature and wind velocity," IEEE Int. Conf. on Acoustics, Speech and Signal Processing, Vol. 4, 1141-1144, 2006.
21. Wiens, T., "Sensing of turbulent flows using real-time acoustic tomography ," 19th Biennial Conf. of the New Zealand Acoustical Society, 2008.
22. Deprez, J.-F., M. Sarafianou, M. Klemm, I. J. Craddock, and P. P. Smith, "Breast imaging through microwave velocity reconstruction preliminary results," Asia Pacific Microwave Conf., 2011.
23. , , , University of Wisconsin Computational Electromagnetics Laboratory, UWCEM Numerical Breast Phantom Repository , http://uwcem.ece.wisc.edu.
24. Klemm, M., J. Leendertz, D. Gibbins, I. J. Craddock, A. Preece, and R. Benjamin, "Towards contrast enhanced breast imaging using ultra-wideband microwave radar system," IEEE Radio and Wireless Symposium, 516-519, New Orleans, USA, 2010.
25. Yee, K., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media ," IEEE Trans. on Antennas and Propagation, Vol. 14, 302-307, 1966.
26. , , , American College of Radiology, Breast Imaging Reporting and Database System (BI-RADS), http://www.acr.org/SecondaryMainMenuCategories/quality safety/.
27. Sarafianou, M., D. R. Gibbins, I. J. Craddock, M. Klemm, J. A. Leendertz, A. Preece, and R. Benjamin, "Breast surface reconstruction algorithm for a multi-static radar-based breast imaging system ," Europ. Conf. on Antennas and Propagation, 1-5, 2010.
28. Duda, R. O., P. E. Hart, and D. G. Stork, Pattern Classification, 2nd Edition, Wiley Interscience, NY, 2000.
29. Yavuz, M. E. and F. L. Teixeira, "Full time-domain DORT for ultrawideband electromagnetic fields in dispersive, random inhomogeneous media," IEEE Trans. on Antennas and Propagation, Vol. 54, No. 8, 2305-2315, 2006.
30. Chen, Y., I. J. Craddock, and P. Kosmas, "Feasibility study of lesion classification via contrast-agent-aided UWB breast imaging," IEEE Trans. on Biomedical Engineering, Vol. 57, No. 5, 1003-1007, 2010.
31. Fang, Q., P. M. Meaney, and K. D. Paulsen, "Microwave image reconstruction of tissue property dispersion characteristics utilizing multiple-frequency information," IEEE Transactions on Microwave Theory and Techniques, Vol. 52, No. 8, 1866-1875, August 2004.