Three-dimensional Distorted Born Iterative Method Enhanced by Breast Boundary Extraction for Microwave Mammography Kazuki Noritake 1 and Shouhei Kidera 1 Abstract— Microwave mammography has several advantages e.g. portability, non-contact and cell-friendly measurement, and low cost for the equipment. Therefore, this technology has been regarded as a more frequent screening technique, than the X- ray based modality. This paper focuses on the dependence of the imaging accuracy, which is obtained using inverse scattering algorithms, on the estimation of the breast boundary. The Envelope method has been proposed as a method of using microwaves to estimate the location of the breast boundary. The accuracy of the boundary estimation via the Envelope method depends on that of the time-delay estimation, which is mostly processed by a filter based on waveform matching between the observed and reference signals. However, the coupling effect between the antenna and breast surface deforms the observed waveforms relative to the reference waveform. To mitigate this problem, this paper introduces the finite-difference time- domain (FDTD)-based waveform correction assuming the three- dimensional (3-D) distorted Born iterative method (DBIM) anal- ysis. The 3-D numerical simulations based on realistic breast phantoms demonstrate that the proposed method enhances the accuracy for the 3-D reconstruction of the dielectric profile in highly heterogeneous cases. Index Terms—Microwave mammography, Distorted born iterative method (DBIM), Envelope-based boundary extraction, FDTD-based waveform correction. I. I NTRODUCTION According to the World Cancer Research Fund (WCRF)[1], breast cancer is the most widely diagnosed type of cancer in women. X-ray mammography is the most popular screening technique for the detection of breast-cancer tumors. However, X-ray mammography presents a risk of harming the cells and demands that the patient’s breasts be subjected to high compression. The unpleasantness of the technique leads to low voluntary examination rates, particularly among young women. Although it is still in the research stage, microwave mammography has attracted considerable attention, being a cell-friendly and compact screening technique that is much less physically pain for the patient. According to an examination of excised breast samples, there is a significant contrast between the dielectric prop- erties of normal tissues (adipose dominant) and malignant tumors[2]. Many imaging algorithms have been developed for tumor detection or characterization; these can be di- vided into the following two categories as confocal (e.g. 1 Graduate School of Informatics and Engineer- ing, University of Electro-Communications, Japan noritake.kazuki@ems.cei.uec.ac.jp kidera@uec.ac.jp beamforming[3]) and inverse scattering algorithms (e.g. Born approximation or distorted Born iterative method (DBIM)[4], contrast source inversion (CSI)[5]). This paper focuses on the DBIM, the effectiveness of which has been demonstrated in number of studies, even if the object has a highly hetero- geneous and dispersive. However, the performance of the DBIM is extremely sensitive to the initial estimate of the dielectric property map and the region of interest (ROI), i.e., the breast boundary[6][7]. Several ROI estimation algorithms are used in medical imaging, such as that based on the resonant frequency shift between the antenna and skin [8]. As a representative ROI estimation algorithm for breast media, the Envelope method has been introduced in the number of studies[9]. Additionally, a similar algorithm specifying the breast boundary, referred to as breast surface identification (BSID), has also been introduced in the literature [10], [11]. However, it should be noted that the successful reconstruc- tion of ROI by the Envelope method relies on the accuracy of the estimations of the range between the antenna and breast surface. In the case of microwave mammography, the range between the antenna and skin surface is within the central wavelength, so the observed waveform is distorted compared to the reference waveform because of the near-field effect or the coupling effect. This waveform mismatch leads to a non-negligible error for range estimation based on waveform matching based filter, e.g. a matched filter. To address the aforementioned issue, a previous study[12] proposed a direct compensation scheme for breast bound- ary estimation using the recovered FDTD recovered signal. Compensation for the range error can be applied directly by assessing the time-shift between the observed and recovered FDTD signals, for which the near-field effect should be considered. This paper extends this method to the three- dimensional (3-D) model, where the multi-static Envelope method is introduced to compensate the reconstruction error of ROI due to sparse array model. The results of FDTD-based numerical simulation using MRI-derived realistic numerical phantoms demonstrate that the proposed algorithm enhances the reconstruction accuracy of the DBIM outputs for highly heterogeneous breast media. II. OBSERVATION MODEL Figure 1 shows the observation model, assumed in the proposed method. Multiple transmitters and receivers array are located along the circumference curve, which surrounds an object area. The breast medium is comprised of skin, adipose, fibro-glandular, and tumor tissues, each of which 978-1-5386-1311-5/19/$31.00 ©2019 IEEE 4819