## 3 Results
### Reconstructions Using the DBIM-TwIST Algorithm  
The observed differences in received signal strength plots due to the target suggest that there is potentially sufficient contrast for an inverse scattering algorithm to reconstruct the target. To test this hypothesis and validate our proposed wideband microwave tomography system, we applied our previously developed DBIM-TwIST algorithm to the data from our experimental measurements as well as CST simulations. The DBIM-TwIST algorithm has been analyzed and validated with numerical microwave breast imaging simulations in previous work [24; 25]. It is based on the distorted Born iterative method (DBIM), which solves the nonlinear scattering problem iteratively by applying a Born approximation at each iteration. The solution to the resulting linear problem is used to update the background medium recursively, until the data residual converges to a minimum [35]. In the DBIM-TwIST algorithm, the linear problem at each DBIM iteration is solved by our own optimized implementation of the two-step iterative shrinkage-thresholding algorithm [24]. The algorithm's  
Figure 9: Received signal strength as a function of receiver number when the array is immersed in 90% glycerine–water for the experimental setup: (**a**) no target and (**b**) water target. forward solver is based on the finite-difference time-domain (FDTD) method, which is applied to a simplified two-dimensional (2-D) model of the tank with line sources at the same locations as the monopoles. The FDTD algorithm is excited with a Gaussian pulse operating in the 0.5-3.5 GHz range, and uses a single-pole Debye model [35] to capture the dispersion of the 90% glycerine-water mixture. To calibrate data from our forward model with CST or experimental data, we apply a standard calibration procedure using the \"empty tank\" datasets [31]. Figure 12 presents complex permittivity reconstructions using the data obtained from simulations and measurements. The images depict the whole tank; however, the reconstruction domain is a ring with a diameter of 120 mm, which is concentric and at 10 mm distance from the antenna array to avoid imaging artifacts from the antennas. Data were collected at the eight transceivers in our system of Figure 4 for both target media, i.e., water and the salt-water mixture. For all reconstructions, cubic voxels of 2.0 mm sides were used in our imaging algorithm. We applied the DBIM-TwIST algorithm with a frequency hopping approach at 1.2, 1.5, 1.8, 2.1, and 2.4 GHz, and performed 20 iterations at each frequency. At the start of the inversion process at 1.2 GHz, the imaging domain was filled with the background glycerine-water medium of known properties. The reconstructed properties at 1.2 GHz were then inserted as the initial guess for the reconstruction at 1.5 GHz, and so on. The total computation time for the forward solver for all eight antennas was 7 s per iteration, and the inversion time was 0.5 s, leading to a total run time of 7.5 s for each DBIM iteration. The Matlab code was run on an Intel i7 3.4 GHz processor with 16 GB RAM memory. Figure 11: Comparison of received signal strength as a function of receiver number from simulations and measurements when the array is immersed in 90% glycerine–water, and targets are introduced. Plots at (**a**) at 1.5 GHz and (**b**) at 2 GHz. Figure 10: Received signal strength as function of receiver number when the array is immersed in 90% glycerine–water and salt–water target is introduced: (**a**) CST simulation; and (**b**) experimental prototype. The actual real and imaginary permittivity values of the water and salt-water targets at 1.2 GHz were measured as \(\epsilon^{\prime}=78.6,\epsilon^{\prime\prime}=4.8\), and \(\epsilon^{\prime}=77.5,\epsilon^{\prime\prime}=30.5\), respectively. The respective values for the background glycerine-water mixture were \(\epsilon^{\prime}=14.2,\epsilon^{\prime\prime}=13.3\).