Mathematical Model for Acousto-Optical Tomography and Its Numerical Simulation / 의학물리

ABSTRACT

In this paper, Acousto-Optical tomography is modeled by a linear integral equation and an inverse problem involving a diffusion equation in n-spatial dimensions. We make two-step mathematical model. First, we solve a linear integral equation. Assuming the optical energy fluence rate has been recovered from the previous equation, the absorption coefficient micro is then reconstructed by solving an inverse problem. Numerical experiments are presented for the case n=2. The traditional gradient descent method is used for the numerical simulations. The result of the gradient descent method produces the blurring effect. To get rid of the blurring effect, we suggest the total variation regularization for the minimization problem.