Mathematical modeling of acousto-optical tomography and its level set simulations

Abstract

Acousto-optical tomography is modeled by using a linear integral equation and an inverse problem involving a diffusion equation in n spatial dimensions, n = 2, 3. Based on measured data, the optical absorption coefficient μ is reconstructed inside a given domain. We make a two-step mathematical model. First, we solve a linear integral equation. Assuming the energy fluence rate has been recovered from the previous equation, we then reconstruct the absorption coefficient μ by solving an inverse problem. Numerical experiments are presented for the case n = 2. We used the level set method for the numerical experiments. At the end, the advantages and the disadvantages of those two methods are mentioned. © 2012 The Korean Physical Society.