Thermoacoustic tomography arising in brain imaging

TL;DR

This paper develops a mathematical model and an explicit inversion formula for thermoacoustic tomography in brain imaging, accounting for sound speed discontinuities across the skull surface.

Contribution

It introduces a new inversion formula for thermoacoustic tomography with variable sound speed, specifically modeling the skull-brain interface.

Findings

Derived an explicit inversion formula as a convergent Neumann series.

Validated the model for cases where all singularities reach the boundary.

Addresses challenges of imaging through discontinuous sound speed regions.

Abstract

We study the mathematical model of thermoacoustic and photoacoustic tomography when the sound speed has a jump across a smooth surface. This models the change of the sound speed in the skull when trying to image the human brain. We derive an explicit inversion formula in the form of a convergent Neumann series under the assumptions that all singularities from the support of the source reach the boundary.