When looking for distributed parameters we have to discretize these unknown functions. Doing so, we reduce the dimension of the problem to something finite. But now, the question is: is there any link between the solution we compute and the one of the initial problem? Then another question: what do we mean with the solution of the initial problem? Since a finite number of data does not allow the determination of an infinity of unknowns, the original data misfit functional has to be regularized to ensure the uniqueness of the solution. Many times, reducing the unknowns to a finite-dimensional space will provide an adequate regularization: the computed solution will look like a discrete version of the solution we were looking for. For example, a naive discretization will often work for solving the deconvolution problem: it will work as long as we do not allow missing frequencies to show up in the numerical solution. But many times, regularization has to be integrated explicitly in the objective function.