Data driven reconstruction using frames and Riesz bases

TL;DR

This paper introduces a data-driven reconstruction method for inverse problems using frames and Riesz bases, generalizing previous algorithms and demonstrating its effectiveness through numerical experiments.

Contribution

It presents a novel data-driven regularization approach based on frames theory, extending existing algorithms with a new orthonormalization procedure for training data.

Findings

The proposed method effectively reconstructs inverse problems.

Numerical experiments show improved accuracy over traditional methods.

The approach generalizes previous algorithms in the literature.

Abstract

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.