Comment "robustifier" les estimateurs par dictionnaire face aux erreurs de grille ?

Let us consider the very general problem of the estimation of a parameter of interest θ ∈ P, where P is a set of continuous values. Sparse based estimation is based on the matching of the parameters of interest to a regular discretization of P, often referred to as the grid. In realistic scenarios, the off-grid error problem is thus inherent to the presence of the grid and limits in a drastic way the estimation performances of the standard sparse estimation algorithms in the high SNR regime where the off-grid error is predominant with respect to the error due to the noise. In this context, numerous contributions in the literature deals with this problem, but according to our knowledge, the proposed approaches can be defined as ad hoc techniques dedicated to a particular estimator. In this work, our objective is to propose a generic post-treatment, called OGEC (Off-Grid Error Correction), in the sense that it can be used to "robustify" against the off-grid problem any existing sparse based estimator. Furthermore, we design this post-treatment to be cheap in term of calculation cost. OGEC being introduced, we derive theoretically its bias and MSE and finally its performances are illustrated in the context of the compressed sampling of non-bandlimited signals.