IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 10, OCTOBER 2013 5343 [10] T. F. Eibert, Ismatullah, E. Kaliyaperumal, and C. H. Schmidt, “Inverse equivalent surface current method with hierarchical higher order basis functions, full probe correction and multilevel fast multipole accelera- tion,” Progr. Electromagn. Res., vol. 106, pp. 377–394, 2010. [11] J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 3rd ed. New York: Springer, 2002. [12] A. Karwowski, “Efcient wide-band interpolation of MoM-derived frequency responses using Stoer-Bulirsch algorithm,” in Proc. IEEE Int. Symp. on Electromagn. Compat., Aug. 2009, pp. 249–252. [13] Y. Ding, K. L. Wu, and D. G Fang, “A broad-band adaptive-frequency- sampling approach for microwave-circuit EM simulation exploiting Stoer-Bulirsch algorithm,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 3, pp. 928–934, Mar. 2003. [14] J. Q. Chen, R. S. Chen, and Z. W. Liu, “Stoer-Bulirsch adaptive fre- quency sampling method for efcient analysis of frequency selective surfaces,” Microw. Opt. Technol. Lett., vol. 50, no. 3, pp. 755–758, Jul. 2007. [15] Y. El-Kahlout and G. Kiziltas, “Effective interpolation scheme for multi-resonant antenna responses: Generalised Stoer-Bulirsch algo- rithm with adaptive sampling,” IET Microw., Antennas and Propag., vol. 5, no. 19, pp. 1849–1856, Jun. 2011. [16] J. Gong and J. L. Volakis, “AWE implementation for electromagnetic FEM analysis,” Electron. Lett., vol. 32, no. 24, pp. 2216–2217, Nov. 1996. [17] A. F. Peterson and M. M. Bibby, An Introduction To The Locally-Cor- rected Nyström Method. San Rafael, CA, USA: Morgan and Clay- pool, 2010. [18] M. S. Tong, Z. G. Qian, and W. C. Chew, “Nyström method solution of volume integral equation for electromagnetic scattering by 3D pen- etrable objects,” IEEE Trans. Antennas Propag., vol. 58, no. 5, pp. 1645–1652, May 2010. [19] S. R. Rengarajan and Y. Rahmat-Samii, “The eld equivalence prin- ciple: Illustration of the establishment of the non-intuitive null elds,” IEEE Antennas Propag. Mag., vol. 42, no. 4, pp. 122–128, Aug. 2000. [20] K. Kottapalli, T. Sarkar, Y. Hua, E. Miller, and G. J. Burke, “Accurate computation of wide-band response of electromagnetic systems uti- lizing narrow-band information,” IEEE Trans. Microw. Theory Tech., vol. 39, pp. 682–687, Apr. 1991. [21] EM Software and Systems, FEKO Suite 6.0 2010 [Online]. Available: http://www.feko.info [22] J. E. Hansen, Spherical Near-Field Antenna Measurements. London: Peter Peregrinus, 1998. [23] M. Serhir, P. Besnier, and M. Drissi, “An accurate equivalent behav- ioral model of antenna radiation using a mode-matching technique based on spherical near eld measurements,” IEEE Trans. Antennas Propag., vol. 56, no. 1, pp. 48–57, Jan. 2008. [24] J. A. Kong, Electromagnetic Wave Theory. Cambridge, MA, USA: EMW Publishing, 2008. Towards Enhancing Skin Reection Removal and Image Focusing Using a 3-D Breast Surface Reconstruction Algorithm Mantalena Saraanou, Ian J. Craddock, and Tommy Henriksson Abstract—Suppressing skin reection is vital for successful tumor detec- tion in radar breast imaging systems. In this communication, a novel skin reection removal (SRR) algorithm is presented based on a previously-pro- posed breast surface reconstruction algorithm. This skin reection removal algorithm is validated using numerical MRI-derived breast models. This communication also investigates how the same skin location information can be used to enhance the delay-and-sum algorithm. Index Terms—Breast cancer detection, microwave radar-based imaging, skin reection suppression. I. INTRODUCTION In radar-based systems for breast cancer detection the measured sig- nals are dominated by the skin reection [1]. This reection should be suppressed e.g., in [2] a perfect background subtraction procedure (measurement with and without the target) was used to calibrate the experimental system. In [3], the calibration signal was obtained by av- eraging the neighboring received signals. In [3] an empty-domain mea- surement was used to calibrate the received signals. However, in reality [2], [3] are unfeasible. Alternatively, in [4], [5] the system may be manually rotated and the measured signal sets subtracted. Although these are practical ap- proaches and [5] has been used in clinical scenarios, they suppose that the skin is largely uniform and symmetrically-tted to the imaging array. Alternative signal processing-based techniques [6]–[9] have been presented for suppressing the skin reection, using methods such as Woody Averaging and Recursive Least Squares (RLS). In [10]–[13], the skin reection signal at a specic antenna was estimated from the ltered versions of the received signals collected at all other antennas. However, all these methods are imperfect as they are sensitive to the uniformity of the skin and may damage the desired tumour signal. In this communication, a novel skin reection removal (SRR) algo- rithm is presented based on the 3-D breast surface reconstruction al- gorithm formulated in [14]. The reconstructed surface is employed to create a voxel-based FDTD breast model, which is used to calculate skin reection signals numerically. The tumour responses are then ob- tained by subtracting these signals from the received signals. The proposed SRR algorithm is evaluated using MRI-derived nu- merical breast models and Bristol’s hemispherical 31-antenna array conguration. The aim is to show that the SRR method yields radar images similar to those obtained from perfect background subtraction, even when the breast surface is not uniform. The communication fo- cuses particularly on the case regularly encountered in clinical trials where it is impossible to arrange the patient’s breast to be perfectly- Manuscript received January 10, 2013; revised May 24, 2013; accepted June 18, 2013. Date of publication June 27, 2013; date of current version October 02, 2013. This work was supported by the Engineering and Physical Sciences Research Council (EPSRC). The authors are with the Department of Electrical and Electronic Engineering, University of Bristol, Bristol BS8 1UB, U.K. (e-mail: M.Saraanou@bristol.ac. uk). Color versions of one or more of the gures in this communication are avail- able online at http://ieeexplore.ieee.org. Digital Object Identier 10.1109/TAP.2013.2271494 0018-926X © 2013 IEEE