# On the Use of Focused Incident Near-Field Beams in Microwave Imaging
## 1 Introduction  
Microwave imaging (MWI) is an imaging technique that can be used to produce a quantitative image of the dielectric profile of the object of interest (OI) by solving the corresponding electromagnetic inverse problem. In MWI, the OI is illuminated by incident electromagnetic fields at the microwave frequency range, and the resulting scattered fields are processed (inverted) to create (reconstruct) the OI's dielectric profile image. This processing often involves calibrating the measured data and applying an appropriate inversion algorithm to this calibrated measured data. This imaging tool has the potential to be utilized for different applications such as breast cancer detection, stroke diagnosis, through wall imaging, security screening, and industrial non-destructive evaluation [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. MWI can also be used in conjunction with other imaging tools, e.g., with magnetic resonance imaging or ultrasound tomography [11; 12; 13]. In addition, MWI can be performed in the time domain or frequency domain, with the latter being the focus of this paper. Moreover, in some applications, reconstructing the magnetic properties is also of interest (e.g., in [14]); herein, we only consider non-magnetic objects. MWI can be performed in at least three fashions: (i) 1D (line reconstruction; e.g., [15]); (ii) 2D (cross section reconstruction; e.g., [16]), and (iii) 3D (volumetric reconstruction; e.g., [17]). This is oftendetermined based on several factors such as the application area, data collection process, and the amount of measured data. For some applications including biomedical imaging, it is desirable to enhance the achievable reconstruction accuracy from MWI. To this end, in addition to the development of appropriate inversion algorithms and regularization techniques, e.g., [18; 19; 20; 21], several other techniques have been suggested to further improve the achievable image accuracy from MWI. For example, these include (i) using prior spatial information about the OI [22; 23; 24], (ii) using prior information about the permittivity values or the expected ratio between the real and imaginary parts of the OI's complex permittivity [25; 26]; (iii) increasing the number of transceivers and frequencies of operation [27]; (iv) improving the signal to noise ratio (SNR) of the system [28]; (v) appropriate data calibration techniques [7; 29]; (vi) enhanced modeling of the imaging system in the inversion algorithm [30]. All of the above techniques may be classified under the following two categories. The first category aims to increase the _overall_ SNR with noise being either the actual noise or the modeling error. (Modeling error is defined as any discrepancies between the actual imaging setup and the numerical model used in the inversion algorithm.) On the other hand, the second category aims to enrich the information content of the data to be used for inversion; this is done by increasing the number of measurements and incorporating prior information (virtual data) about the OI. The work presented in this paper aims to suppress the effect of _undesired_ scatterers in the inversion process. To this end, we begin by defining undesired scatterers as any scatterers within the imaging chamber in which we are _not_ interested in finding their _unknown_ dielectric properties. Considering the scattered fields due to these undesired scatterers as unwanted signals, or _noise_, the topic of this paper, therefore, falls under the first category above: i.e., enhancing the overall SNR. Note that the undesired scatterer and the OI might be two distinct objects, or they can be attached to each other. For example, in 2D (cross-sectional) imaging of a 3D object, e.g., breast, the irradiating antenna not only illuminates the cross-section of interest but also illuminates other cross-sections. These other cross sections are then undesired scatterers with respect to the cross section to be imaged.