A quantitative imaging method is proposed based on microwave measurements where a direct inversion in real space is employed. The electrical properties of penetrable objects are reconstructed using a resolvent kernel in the forward model, which is extracted from calibration measurements. These measurements are performed on two known objects: the reference object (RO) representing the scatterer-free measurement and the calibration object representing a small scatterer embedded in the RO. Since the method does not need analytical or numerical approximations of the forward model, it is particularly valuable in short-range imaging, where analytical models of the incident field do not exist while the fidelity of the simulation models is often inadequate. The experimentally determined resolvent kernel inherently includes the particulars of the measurement setup, including all transmitting and receiving antennas. The inversion is fast, allowing for quasi-real-time image reconstruction. The proposed technique is demonstrated and validated through examples using simulated and experimental data. Its performance with noisy data is also examined. The concept of experimentally determined resolvent kernel in the forward model may be valuable in other imaging modalities such as ultrasound, photonic imaging, electrical-impedance tomography, etc.

Two real-time reconstruction algorithms, i.e., quantitative microwave holography and scattered-power mapping, have been shown to be successful in the imaging of compressed tissue of relatively small thicknesses such as 1 and 2 cm. In both cases, planar data acquisition of frequency-swept transmission coefficients has been employed. Despite the fact that these algorithms are based on a linear forward model of scattering, they have been capable of providing quantitative estimates of the tissue permittivity due to the experimentally derived kernel of the scattering integral. Here, we demonstrate similar performance with a thicker (approximately 5 cm) compressed-breast phantom. This thickness is greater than or comparable to the median thickness employed in mammography, depending on the view (craniocaudal or mediolateral oblique). The two methods are described in a common mathematical framework for the first time. The importance of the system calibration and the choice of a host medium are discussed through experiments. A new method for focusing onto suspect regions is demonstrated. The limitations of real-time imaging are highlighted, along with an outlook to improve the image resolution and suppressing artifacts without sacrificing the reconstruction speed. Future work aims at validation with high complexity, realistic compressed-breast phantoms.

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