Ultrasound-modulated optical tomography

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 ? 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 ? 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.