Mathematical Modeling of Acousto-Optical Tomography and its Level Set Simulations

다국어 초록 (Multilingual Abstract)

Acousto-Optical Tomography is modeled by a linear integral equation and an inverse problem involving a diffusion equation in n spatial dimensions, <I>n</I> = 2, 3. Based on measured data, the optical absorption coefficient <I>μ </I>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 <I>μ</I> is then reconstructed by solving an inverse problem. Numerical experiments are presented for the case <I>n</I> = 2. We used the level set method for the numerical experiments. At the end, advantages and disadvantages of those two methods are mentioned.

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