## 5 Conclusions  
In this study, we investigated the ability of an optimization procedure to enhance the quality of TFM images of point-like reflectors inside unknown anisotropic and inhomogeneous nuclear welds. The procedure was first evaluated with simulated data and it was shown that it was able to correct the degradation of the image due to the unknown material properties, with good performance. The defect echoes were accurately estimated with less than 1 mm errors, although it was also observed that the estimation of the material properties could not be precisely achieved. The dispersion of the results with a value of 26%, which was a consequence of the optimization only being realized around a single isolated defect, was way too strong to provide a fair characterization of the whole structure. The properties estimation was then only reliable in the region around the reflector. Moreover, a sensitivity analysis demonstrated that the several unknown parameters of the weld model were correlated with one another and that their respective contributions were mainly driven by their mutual interactions rather than by their single effect. Therefore, a great variety of combinations was solution to the optimization problem.  
An experimental application of the procedure with two samples from a same weld confirmed the results of the numerical proof of concept. The reflectors were hardly visible on the images computed with an isotropic reconstruction model, but after the optimization, the two defects were clearly visible and their localization was well estimated. Here again, the final images were of very satisfactory quality with positioning errors inferior to 1 mm, but the material estimation was not accurate due to the substantial dispersion, which was upwards of 15%. A cross-comparison of the material properties after optimization indicated that there was no common weld model between the two experimental cases. It was however found that one model taken from one result on the second sample was able to correct the image in both cases. Nevertheless, our aim was to implement an optimization procedure to correct the images and, as such, the proposed approach emphatically succeeds at this task.  
Several methods of improvement are considered for future works. The main challenge is to reduce the computation times needed for the optimization. This should be achieved by further tuning the hyper-parameters of the particle swarm algorithm to reduce the number of iterations needed to reach an optimal result, and by using the CUDA architecture to parallelize the computations in order to shorten the time needed by CIVA to compute the images. Some interest has also to be taken in the _a priori_ information that we can use to reduce the exploration space range and thus to reduce the dispersion of the results. Finally, the optimization procedure should be evaluated for crack-type defects that are of real concern in the NDT domain.  
Conceptualization, C.M., S.R. and D.L.; methodology, C.M., S.R.; software, C.M.; validation, C.M. and S.R.; formal analysis, C.M.; investigation, C.M.; data curation, C.M.; writing--original draft preparation, C.M.; writing--review and editing, C.M., S.R. and D.L.; visualization, C.M.; supervision, S.R. and D.L.; project administration, S.R. and D.L.; funding acquisition, S.R. All authors have read and agreed to the published version of the manuscript.  
This study is part of European project ADVISE, that has received funding from the Euratom research and training programme 2014-2018 under grant agreement No. 755500.  
The authors would like to thank the ADVISE project partners, with special credits to Electric De France (EDF) for providing mock-ups to all consortium partners.  
The authors declare no conflict of interest.