| Ultrasound-modulated optical tomography is modeled by 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 mu is reconstructed inside of 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, the absorption coefficient mu is then reconstructed by solving an inverse problem. Numerical experiments are presented for the case n = 2. Two methods are used for the numerical experiments, gradient descent and levelset. At the end, advantages and disadvantages of those two methods are mentioned. |
