Integral equation models for thermoacoustic imaging of dissipative tissue

Abstract

In case of non-dissipative tissue the inverse problem of thermoacoustic imaging basically consists of two inverse problems. First, a function $ϕ$ 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 $ϕ$. In case of dissipative tissue, it is no longer possible to calculate explicitly the projection of $ϕ$ 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 $ϕ$. The advantage of this approach is that all known reconstruction formulas for $ϕ$ from the respective projection can be exploited.