Limited Angle Acousto-Electrical Tomography

TL;DR

This paper investigates the limited angle acousto-electrical tomography problem, proposing an optimization-based reconstruction method, analyzing stability and ill-posedness, and demonstrating numerical results in 2D with simulated data.

Contribution

It introduces a Hilbert space formulation and Landweber iteration for limited angle acousto-electrical tomography, providing numerical analysis and stability insights.

Findings

Features near the boundary are stably reconstructed.

Features farther from the boundary are less accurately reconstructed.

The ill-posedness is quantified via singular value decomposition.

Abstract

This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from different prescribed boundary conditions. Particular emphasis is placed on the limited angle scenario, in which the boundary conditions are supported only on a part of the boundary. The reconstruction problem is formulated as an optimization problem in a Hilbert space setting and solved using Landweber iteration. The resulting algorithm is implemented numerically in two spatial dimensions and tested on simulated data. The results quantify the intuition that features close to the measurement boundary are stably reconstructed and features further away are less well reconstructed. Finally, the ill-posedness of the limited angle problem is quantified numerically using the singular value decomposition of the corresponding linearized problem.