## 6 Conclusions and Future Work  
Microwave breast imaging assumes that an estimate of the effective average dielectric properties can be found and used to synthetically focus the backscattered signals. Errors in the estimate of effective average dielectric properties reduce coherent addition at dielectric scatterer locations, leading to poorer image quality and increased localisation errors. Patient studies with microwave radar imaging to date have used a single estimate determined in advance from experimental studies or published dielectric properties studies.  
Due to the importance of the effective average dielectric properties on image quality, parameter search algorithms have been proposed as a method to determine this patient-specific value. Parameter search algorithms rely on correctly reconstructed images having identifiable properties. These methods do not rely on a given propagation path being representative of the imaging volume as a whole, and are not affected by problems with multipath propagation unlike the previously used transmission-based methods.  
This work identifies properties of images reconstructed with over- and underestimated average dielectric properties. In particular, when underestimating the effective average dielectric properties, it was found that the apparent location of the response moves towards the edge of the imaging domain and that the spatial frequency content of the microwave breast image decreases. Conversely, as the effective average dielectric properties were overestimated, the apparent location of the response moves towards the centre of the imaging domain and the spatial frequency content of the microwave breast image increases. FQMs, common in digital camera autofocus, were identified as potentially suitable fitness functions, as they estimate the spatial frequency content of images.  
Many FQMs were found to reward high quality images, indicating that this type of metric is suitable for average dielectric properties estimation. In particular, gradient-based metrics are computationally simple, have a well-understood method of action and are suitable fitness functions, such as the Gaussian Energy, \(\phi^{\text{G}}_{\text{GSS}}\). These results from dielectrically heterogeneous phantoms with different tumour sizes indicate that parameter search algorithms using FQMs as fitness functions are suitable for estimating the average dielectric properties for microwave breast imaging.  
Future work should evaluate clinical data gathered from patient studies, both healthy and with disease, to ensure that the algorithms are robust to a wide range of tissues and clinical scenarios, including healthy cases.  
This work was supported by the Irish Research Council (Grant No. RCS1326), Science Foundation Ireland (Grant No. 12/IP/1523 and 11/SIRG/I2120), the MiMED COST Action (TD1301) and the European Research Council under the European Union Horizon 2020 Programme (H2020)/ERC grant agreement number 637780.  
[PERSON] and [PERSON] designed and performed the experiments; [PERSON] contributed signal processing analysis tools; [PERSON] designed the antennas used in the experiment; [PERSON] analysed the data and wrote the paper; and [PERSON], [PERSON] and [PERSON] supervised the work, including experimental design, analysis and writing.  
The authors declare no conflict of interest.