Integral equation models for thermoacoustic imaging of dissipative tissue

TL;DR

This paper develops integral equation models for thermoacoustic imaging in dissipative tissue, enabling the estimation of electromagnetic absorption functions despite tissue dissipation effects.

Contribution

It derives integral equations for each pressure data type, facilitating the use of existing reconstruction formulas in dissipative tissue imaging.

Findings

Integral equations for spherical, circular, and planar pressure data.

Enables reconstruction of electromagnetic absorption in dissipative tissue.

Extends thermoacoustic imaging methods to more realistic tissue models.

Abstract

In case of non-dissipative tissue the inverse problem of thermoacoustic imaging basically consists of two inverse problems. First, a function $\phi$ depending on the \emph{electromagnetic absorption function}, is estimated from one of three types of projections (spherical, circular or planar) and secondly, the \emph{electromagnetic absorption function} is estimated from $\phi$. In case of dissipative tissue, it is no longer possible to calculate explicitly the projection of $\phi$ from the respective pressure data (measured by point, planar or line detectors). The goal of this paper is to derive for each of the three types of pressure data, an integral equation that allows estimating the respective projection of $\phi$. The advantage of this approach is that all known reconstruction formulas for $\phi$ from the respective projection can be exploited.