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Abstract:
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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
μ 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
μ 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. |
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