Imaging neutron capture cross sections: i-TED proof-of-concept and future prospects based on Machine-Learning techniques

i-TED is an innovative detection system which exploits Compton imaging techniques to achieve a superior signal-to-background ratio in ($n,\gamma$) cross-section measurements using time-of-flight technique. This work presents the first experimental validation of the i-TED apparatus for high-resolution time-of-flight experiments and demonstrates for the first time the concept proposed for background rejection. To this aim both $^{197}$Au($n,\gamma$) and $^{56}$Fe($n, \gamma$) reactions were measured at CERN n\_TOF using an i-TED demonstrator based on only three position-sensitive detectors. Two \cds detectors were also used to benchmark the performance of i-TED. The i-TED prototype built for this study shows a factor of $\sim$3 higher detection sensitivity than state-of-the-art \cds detectors in the $\sim$10~keV neutron energy range of astrophysical interest. This paper explores also the perspectives of further enhancement in performance attainable with the final i-TED array consisting of twenty position-sensitive detectors and new analysis methodologies based on Machine-Learning techniques.