Iterative regularization for constrained minimization formulations of nonlinear inverse problems

TL;DR

This paper explores iterative regularization methods for solving constrained minimization problems in nonlinear inverse problems, including applications to diffusivity identification and impedance acoustic tomography, with convergence analysis and numerical experiments.

Contribution

It introduces a convergence analysis framework for iterative regularization in constrained nonlinear inverse problems and applies it to novel hybrid imaging techniques.

Findings

Convergence of iterative methods is established for the inverse problems considered.

Numerical experiments demonstrate effectiveness in impedance acoustic tomography.

Application to diffusivity identification shows practical viability.

Abstract

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss applicability to the problem of identifying the spatially varying diffusivity in an elliptic PDE from different sets of observations. Among these is a novel hybrid imaging techology known as impedance acoustic tomography, for which we provide numerical experiments.