Inverse problems in spaces of Radon measures

In this work, we study the inverse problem of recovering an unknown sparse source u from a noisy observation y of its image through a known linear forward operator G. First, we study the source identification problem by considering a TV-norm regularized problem. In this case, our focus is to optimize the placement of measurement points at which data are collected, such that the uncertainty in the estimated parameters is minimized. More precisely, we introduce an optimal design criterion for the sparse inverse problems based on a linearization of the forward operator G. Finally, some numerical results are given to demonstrate that presented method is computationally efficient and accurate.