Multi-frequency Integration Algorithm of Contrast Source Inversion Method for Microwave Breast Tumor Detection* Hiroki Sato 1 and Shouhei Kidera 1 Abstract— Microwave mammography is one of the most promising alternatives to X-ray-based breast cancer detection techniques, where a malignant tumor has a certain level of dielectric property contrast compared with those in normal tissues. However, the inverse problem of reconstructing complex permittivity is a non-linear and ill-posed problem, and the appropriate selection of such algorithms is the key to the success of microwave mammography. The contrast source inversion (CSI) method is the most promising solution to the above problem, where the iterative procedure does not require a computationally expensive forward solver, like the finite difference time domain (FDTD) method. However, the conventional CSI method assumes a non-dispersive dielectric model, while breast or other human tissues have a non- negligible dispersive property. To address this problem, this paper introduces an extended CSI method, which is suitable for dispersive medium and in which multi-frequency integration is introduced to enhance the reconstruction accuracy. The FDTD numerical test, which uses a realistic breast phantom via magnetic resonance imaging (MRI), demonstrates that our proposed method efficiently enhances the reconstruction accuracy even in dispersive medium. I. INTRODUCTION Recent reports from the World Cancer Research Fund have revealed that breast cancer has become one of the most widely diagnosed cancers in women [1]. Microwave-based breast cancer detection, known as microwave mammography, is one of the promising options for frequent screening for cancer, which may be used as an alternative to the traditional X-ray mammography, ultrasound, and magnetic resonance imaging (MRI) in terms of cost, compactness, and safety. While X-ray mammography is the most commonly used imaging modality, it has a serious risk because of X- ray exposure to normal cells [2]. Ultrasound imaging has some advantages in terms of cost, portability, and suitability, especially for women with dense breasts [3]. The MRI-based modality has disadvantages in terms of its high cost and the large equipment required [4]. Microwave mammography is based on the clinical fact that there is a significant dielectric property contrast between nor- mal and malignant tissue in breasts at microwave frequencies. M. Lazebnik et al. demonstrated that there is a significant dielectric property contrast between normal and malignant tissue when measuring excised breast tissue specimens [5]. J. D. Shea et al. also revealed that the dispersion property *This research and development work was supported by the MIC/SCOPE 162103102. 1 H. Sato and S. Kidera are with Graduate School of Informatics and Engineering, University of Electro-Communications, Tokyo, Japan kidera@uec.ac.jp and fitting parameters using the single-pole Debye model [4] for the complex permittivity of breast tissue are from 0.5 to 3.5 GHz [6]. Microwave imaging algorithms are mainly divided into two categories: the radar-based approach and the tomographic approach. Studies have shown that [7] the space-time beamforming-based radar approach has successfully demonstrated its effectiveness by processing a number of tumor reflections. However, this method suffers from a lower contrast image when the malignant tumor is buried in the fibroglandular tissue, which has the same level of dielectric property as cancer. In contrast, the tomographic approach is considered more promising because a complex dielectric map can be recon- structed by solving the domain integral equation. However, the above integral equation cannot be solved easily because it is non-linear and an ill-posed problem. In particular, conventional Born approximation-based methods, such as diffraction tomography [8], suffer from inaccuracy in dealing with the dielectric property map that has a much higher contrast than the background medium. Among the numerous inverse scattering algorithms, the distorted Born iterative method (DBIM) is one of the most promising algorithms because it updates the background profile to maintain the linearity of the problem. Some literature has shown that the DBIM offers accurate results even for dispersive breast medium, including cancer [9], [10], [11]. However, the DBIM basically requires a forward solver in each iterative step, and it would take an enormous amount of computation, especially for dealing with a three-dimensional problem. Considering this background, we focused on the contrast source inversion (CSI) method [12], which also solves the non-linear integral equation by iteration steps. However, the CSI does not require a computationally expensive forward solver, such as FDTD; instead, it simultaneously solves the state and data equation. In addition, a multiple frequency strategy for the CSI method, such as frequency hopping, was developed for accuracy enhancement in refs. [13], [14]. However, there are very few studies that have focused on the CSI method and that dealt with a frequency-dependent dielectric object, such as breasts or other human tissues. To address this problem, this paper introduces a multi- frequency integration scheme for the CSI method for dis- persive breast medium [13]. This method first reconstructs the complex permittivity map for each frequency using the traditional CSI method, and the frequency-dependent characteristic is sequentially determined by the single-pole Debye model. In addition, this method integrates the multi- frequency CSI outputs by considering the Debye curve using 978-1-5386-1311-5/19/$31.00 ©2019 IEEE 1863