  We study the problem of regularization of inverse problems adopting a purely
data driven approach, by using the similarity to the method of regularization
by projection. We provide an application of a projection algorithm, utilized
and applied in frames theory, as a data driven reconstruction procedure in
inverse problems, generalizing the algorithm proposed by the authors in Inverse
Problems 36 (2020), n. 12, 125009, based on an orthonormalization procedure for
the training pairs. We show some numerical experiments, comparing the different
methods.
