Estimation of optical absorption in anisotropic background
Estimation of optical absorption in anisotropic background
复制标题
各向异性背景中光吸收的估计
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
E. Somersalo
中科院分区：
文献类型：
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作者：
J. Heino;E. Somersalo
本文提出了一个各向异性光传输模型，并在各向异性存在的情况下重建了光吸收系数。为了模拟的各向异性，我们推导出在各向异性的情况下的扩散方程，并提出了扩散矩阵的特征值分解。本文考虑的反问题是在各向异性方向已知但强度可能变化的情况下估计光吸收。为了解决这个逆问题，采取了两种方法。首先，我们假设各向异性的强度是已知的，当强度值正确和不正确时，使用强度的固定值比较最大后验重建。然后，我们通过选择强度的先验分布和计算边缘后验密度来扩展解决方案，以允许各向异性强度的不确定性。最大后验估计的数值例子再次提出。本文的结果表明，各向异性的身体是一个属性，不能忽略的吸收系数的估计。
In this paper we present a model for anisotropic light propagation and reconstructions of optical absorption coefficient in the presence of anisotropies. To model the anisotropies, we derive the diffusion equation in an anisotropic case, and present the diffusion matrix as an eigenvalue decomposition. The inverse problem considered in this paper is to estimate the optical absorption when the directions of anisotropy are known, but the strength may vary. To solve this inverse problem, two approaches are taken. First, we assume that the strength of anisotropy is known, and compare maximum a posteriori reconstructions using a fixed value for the strength when the value for the strength is both correct and incorrect. We then extend the solution to allow an uncertainty of the strength of the anisotropy by choosing a prior distribution for the strength and calculating the marginal posterior density. Numerical examples of maximum a posteriori estimates are again presented. The results in this paper suggest that the anisotropy of the body is a property that cannot be ignored in the estimation of the absorption coefficient.