On regularization methods for inverse problems of dynamic type

TL;DR

This paper introduces new regularization methods for dynamic linear inverse problems using dynamic programming, providing theoretical convergence results and demonstrating effectiveness through a numerical example in dynamic EIT.

Contribution

It develops novel regularization techniques based on dynamic programming for dynamic inverse problems, with proven regularization properties and convergence rates.

Findings

Proved regularization properties for the new methods

Established convergence rates for both approaches

Validated methods with a dynamic EIT numerical example

Abstract

In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are followed: a continuous and a discrete one. We prove regularization properties and also obtain rates of convergence for the methods derived from both approaches. A numerical example concerning the dynamic EIT problem is used to illustrate the theoretical results.