A \(\varGamma \)-Convergence Result and An Off-the-Grid Charge Algorithm for Curve Reconstruction in Inverse Problems

Several numerical algorithms have been developed in the literature and employed for curves reconstruction. However, these techniques are developed within the discrete setting, namely the super-resolved image is defined on a finer grid than the observed images. Conversely, off-the-grid (or gridless) optimisation does not rely on a fine grid and offer a tractable theoretical and numerical framework. In this work, we present a gridless method accounting for the reconstruction of both open and closed curves, based on the latest theoretical development in off-the-grid curve reconstruction. This paper also shows \(\varGamma \) $\Gamma$ -convergence results of the discretised surrogate functional towards the continuous energy we coined CROC.