Regularization by dynamic programming

TL;DR

This paper explores continuous regularization techniques for linear inverse problems using dynamic programming, establishing their regularization properties and convergence rates, with a numerical EIT example demonstrating practical effectiveness.

Contribution

It introduces a novel regularization approach based on dynamic programming for linear inverse problems, providing theoretical analysis and convergence rates.

Findings

Proved regularization properties of the proposed methods

Established convergence rates for the algorithms

Demonstrated effectiveness through a numerical EIT example

Abstract

We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization properties and also obtain rates of convergence for our methods. A numerical example concerning a dynamical electrical impedance tomography (EIT) problem is used to illustrate the theoretical results.