## 2 Materials and Methods
### Warelia MBI: Parametric Radar Image Formation
The geometry is exploited to split the imaging scene in \"Out of breast\" and \"In breast\" segments and further estimate \(\mathrm{\hat{d}_{OutOfBreast,i,p}}\) and \(\mathrm{\hat{d}_{InBreast,i,p}}\) for each transceiver i and each pixel p in the imaging scene. The critical elements of the tailored implementation of TR-MUSIC in the Wavelia QIF are summarized below and in the flowchart of Figure 1.  
* Sectorization of the imaging scene: Considering the high level of heterogeneity of the breast tissues, but also the potentially irregularly shaped breast tumours, MBI image formation is performed using sectorized subsets of the circular sensor network of the Wavelia MBI system, at each vertical scan position. Both the physical size of the sensor sub-array (sector) and the number Ns of sensors used for the elementary sub-image formation is critical to the achievable performance of the MBI system, in terms of unambiguous detection and valid characterization of breast lesions. Ns = 6 was fixed in the Wavelia QIF for the FiH clinical investigation. * Sensor fidelity zone setting: Bounding the portion of the imaging scene, being efficiently illuminated by each sensor sub-array. In the current implementation of the  
Figure 1: Wavelia MBI radar image formation: the critical parameters. Wavelia QIF, a spatial filter activates the contribution of a given antenna to a given pixel p in the imaging scene, only if the Euclidean distance between the pixel and the phase centre of the antenna is inferior to a pre-set value d\({}_{\text{max}}\). * Automated, data-driven, frequency selection for imaging: The TR-MUSIC imaging is performed per frequency. In the Wavelia QIF, a limited number of frequency points is automatically selected for imaging in each azimuthal sector of illumination, based on the information content of the MFRM at each frequency. The employed frequency selection criterion was previously defined in [15]. * pc_fib parameter setting in multiple search ranges: A large variability exists in the dielectric properties of each breast tissue type over the population, as demonstrated by multiple studies involving ex-vivo dielectric measurements of a large sample of excised breast tissues [18; 19; 20; 21]. Considering that the full dielectric map of each breast cannot become practically available, data-driven techniques are employed in the Wavelia QIF to deduce the unknown dielectric properties of the healthy breast tissue in each breast, by assessing the pc_fib parameter. The pc_fib parameter, which is involved in the formulation of the illumination vector of the MBI sensor array, is physically associated with the percentage of fibro-glandular tissue along the propagation path within the breast, from a given transmitting antenna to the interrogated imaging pixel and back to a given receiving antenna, as defined in Equations (1)-(3). The Wavelia QIF generates a set of parametric MBI radar images under various assumptions on pc_fib. The generated set of parametric images is further evaluated in terms of focusing, using the image curvature [22; 23] as a focusing quality measure. To better handle the heterogeneity of the breast and potentially better reveal the non-uniform angular response of the breast lesions to MBI, the pc_fib parameter setting is performed independently in each azimuthal imaging sector, while employing multiple search ranges. In the Wavelia QIF, X1 wide and X2 narrow pc_fib parameter search ranges are systematically employed for image formation, thus a total number of X = (X1 + X2) MBI images are formed per patient's breast. The wide pc_fib search ranges result in 3D MBI images including the most complete representations of the detected breast lesion shape. The narrow pc_fib search ranges are expected to lead to partial representations of the detectable breast lesions.