## 1 Introduction  
In recent years, microwave imaging has shown promising results in early breast imaging clinical trials. In particular, an ongoing study with over 200 patients shows sensitivities equivalent to mammography, and slightly higher than mammography in dense breasts [1; 2]. Other studies have analysed the variability of measurements of healthy volunteers over time-frames of two to eight months and analysed the comfort levels of patients [3]. Previous studies have also shown for eight patients with and without disease that the reconstructed images are consistent with the clinical history of the patient [4]. In general, microwave radar imaging for breast cancer can be considered analogous to synthetic aperture radar, where a synthetic aperture array of non-directional antennas sequentially illuminates the imaging domain and backscattered signals are collected either at the transmitting antenna (monostatic) or at the transmitting antenna and other receivers (multistatic). These backscattered signals are then synthetically focused to points within the imaging domain and the energy of the summed signal used as the intensity of the point. At points where dielectric scatterers are located, coherent addition occurs resulting in a larger energy than the surrounding area. This technique relies on a number of assumptions:  
1. that sufficient contrast exists between cancerous and healthy tissues [5];that large reflections due to the skin can be isolated and removed [6; 7; 8; 9];
* and that the backscattered signals can accurately be synthetically focused to points within the imaging domain [10; 11; 12; 13; 14]. No consensus exists in the literature on the expected contrast in dielectric properties between cancerous and healthy breast tissues in the microwave frequency band from 0.5 to 10 GHz. Initial studies indicated an expected contrast in dielectric properties of cancerous and healthy tissues of between 2.3:1 and 10:1, and extensive reviews of these early studies have been published [15; 16; 17; 18; 19]. However, in 2007, the largest and most comprehensive study to date suggested the contrast in dielectric properties of cancerous and healthy breast tissues could be as low as 1.1:1 [20; 21]. This motivated research of suitable contrast agents which could be used for differential imaging and a number of promising results have been demonstrated in the literature [22; 23; 24; 25; 26; 27]. Additionally, a number of studies on dielectric properties measurement have examined factors that could impact the measurement, such as differences between _ex vivo_ and _in vivo_ dielectric properties measurement [28; 29; 30; 31]; histological analysis of the tissue samples [32]; and the sensing depth of the metrological techniques used [33; 34]. These recent studies on dielectric properties measurement, in addition to promising reported results from ongoing patient imaging trials [1; 2], indicate that the expected contrast in the context of microwave imaging, might not be as low as measured in [20; 21]. This work considers the assumption that backscattered signals can accurately be synthetically focused to points within the imaging domain. Specifically, this work analyses the effect that incorrectly estimating the average dielectric properties has on image quality. The average dielectric properties estimate is the main contributing factor to focusing accuracy [35]. To date, one effective average dielectric property has been chosen _a priori_ for patient imaging studies [1; 2; 3; 4]. However, this parameter is known to be patient-specific [13; 36]. Due to the importance of the effective average dielectric properties as an imaging parameter, a number of methods have been considered to estimate the effective average dielectric properties accurately in simulation and experimental studies [10; 14; 36; 37].