## 5 Results
### Initial Evaluation  
To determine the most suitable FQMs, all FQMs were evaluated for the 5 targets in Figure 2b using the dielectrically homogeneous phantom. The mean value of the evaluation criteria (\(\Delta\varepsilon_{r}\), \(\Delta\mathbf{r}\), \(\mathrm{SMR}(I_{\varepsilon_{r}^{\mathrm{W}}})\) and \(\mathrm{SCR}(I_{\varepsilon_{r}^{\mathrm{W}}})\)) is shown in Table 2. Metrics are listed in order of rank for each method of action, and this rank is shown. Also shown is a global rank which is useful for comparing the different methods of action. Of all the metrics analysed, two metrics perform very well as fitness functions: the Central Moment, \(\phi^{\mathrm{S}}_{\mathrm{ACM}}\), and the Gaussian Energy, \(\phi^{\mathrm{G}}_{\mathrm{GSS}}\). The Central Moment, \(\phi^{\mathrm{S}}_{\mathrm{ACM}}\), rewards images that are closest to the average dielectric properties, being on average within \(\Delta\varepsilon_{r}=0.7\) of the known value of \(\varepsilon_{r}=6\). However, the Gaussian Energy, \(\phi^{\mathrm{G}}_{\mathrm{GSS}}\), rewards images that are of a high quality, rewarding images that have the best localisation error, \(\Delta\mathbf{r}\), and the best clutter suppression, \(\mathrm{SMR}(I_{\varepsilon_{r}^{\mathrm{W}}})\) and \(\mathrm{SCR}(I_{\varepsilon_{r}^{\mathrm{W}}})\). Other metrics based on the gradient, \(\phi^{\mathrm{G}}\), or statistics, \(\phi^{\mathrm{S}}\), of the image also reward images of high quality; ten of the top eleven metrics use these methods of action. All metrics based on the Laplacian of the image, \(\phi^{\mathrm{L}}\), perform very similarly, selecting images with almost the same accuracy, \(\Delta\varepsilon_{r}\), localisation error, \(\Delta\mathbf{r}\), and clutter suppression, \(\mathrm{SMR}(I_{\varepsilon_{r}^{\mathrm{W}}})\) and \(\mathrm{SCR}(I_{\varepsilon_{r}^{\mathrm{W}}})\). Five more metrics perform very similarly to metrics based on the Laplacian, \(\phi^{\mathrm{L}}\): three based on the gradient of the image, \(\phi^{\mathrm{G}}\), the Tenengrad mean, \(\phi^{\mathrm{T}}_{\mathrm{M}}\), the Squared Gradient, \(\phi^{\mathrm{G}}_{\mathrm{DMS}}\), and the Gradient Energy, \(\phi^{\mathrm{G}}_{\mathrm{GSS}}\); and two based on wavelet decomposition of the image, \(\phi^{\mathrm{W}}\), the Detail Variance, \(\phi^{\mathrm{W}}_{\mathrm{V}}\), and the Absolute Detail Sum, \(\phi^{\mathrm{W}}_{\mathrm{AS}}\). The two metrics based on the Fourier transform, \(\phi^{\mathrm{F}}\), do not perform well as fitness functions in these scenarios, identifying images with poor clutter suppression, \(\mathrm{SMR}(I_{\varepsilon_{r}^{\mathrm{W}}})\) and \(\mathrm{SCR}(I_{\varepsilon_{r}^{\mathrm{W}}})\). Additionally, the Fourier-based metrics, \(\phi^{\mathrm{F}}\), select images with localisation errors that are, on average, greater than \(10\,\mathrm{mm}\), \(\Delta\mathbf{r}>10\,\mathrm{mm}\). As shown in Figure 4, images generated with underestimated effective average dielectric properties, \(\sqrt{\frac{\varepsilon_{r}^{\mathrm{T}}}{\varepsilon_{r}}}<1\), are characterised by large responses much closer to the skin than the true scatterer location. Metrics based on the Fourier transform, \(\phi^{\mathrm{F}}\), reward these images resulting in poor performance [44]. Metrics based on the Fourier transform, \(\phi^{\mathrm{F}}\), were first proposed for low-contrast images where they can be more effective [71], whereas the contrast for microwave radar images is higher. Although the AC-DC Reduced Ratio, \(\phi^{\mathrm{F}}_{\mathrm{RR}}\), performed better in noisy images than the AC-DC Ratio, \(\phi^{\mathrm{F}}_{\mathrm{RR}}\) in experimental images, that was not found for microwave radar images. Figure 4: Coronal slices of the experimental PSF at the tumour location. The maximum intensity of images (**a**,**c**) are 40% and 9% of image (**b**). The normalised images with linear colour scales are displayed so that features can be more clearly identified.