Work

Continuity of the Linearized Forward Map of Electrical Impedance Tomography from Square-Integrable Perturbations to Hilbert–Schmidt Operators

Year: 2025

Type: article

Abstract: . This work considers the Fréchet derivative of the idealized forward map of two-dimensional electrical impedance tomography, i.e., the linear operator that maps a perturbation of the coefficient in the conductivity equation over a bounded two-dimensional domain to the linear approximation of the corresponding change in the Neumann-to-Dirichlet boundary map. It is proved that the Fréchet derivative is bounded from the space of square-integrable conductivity perturbations to the space of Hilbert–Schmidt operators on the mean-free [Formula: see text] functions on the domain boundary if the background conductivity coefficient is constant and the considered simply-connected domain has a [Formula: see text] boundary. This result provides a theoretical framework for analyzing linearization-based one-step reconstruction algorithms of electrical impedance tomography in an infinite-dimensional setting.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/24m1703136

Authors: Joanna Bisch, Markus Hirvensalo, Nuutti Hyvonen

Institution: Aalto University

Language: English

Topic: Electrical and Bioimpedance Tomography

Subfield: Electrical and Electronic Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Academy of Finland

Awards: Centre of Excellence of Inverse Modelling and Imaging, Flagship of Advanced Mathematics for Sensing, Imaging and Modelling