Inverse transport with isotropic sources and angularly averaged measurements

Inverse transport with isotropic sources and angularly averaged measurements
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具有各向同性源和角平均测量的逆传输

DOI：
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发表时间：
2008
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通讯作者：
F. Monard
F. Monard
中科院分区：
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文献类型：
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作者：
G. Bal;I. Langmore;F. Monard

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我们考虑空间相关散射的重建 扩散型线性迁移方程中的系数 测量.在此设置中，对测量的贡献为 散射核对谐波乘积的积分 函数，加上一个附加项，当吸收和 散射很小。线性化问题是严重不适定的。 我们构造了一个正则化的逆，允许重建 散射核的低频成分，高达二次 误差，来自非线性映射。迭代方案用于 改善这种误差，使其在高频时很小 散射核的含量小。
We consider the reconstruction of a spatially-dependent scattering coefficient in a linear transport equation from diffusion-type measurements. In this setup, the contribution to the measurement is an integral of the scattering kernel against a product of harmonic functions, plus an additional term that is small when absorption and scattering are small. The linearized problem is severely ill-posed. We construct a regularized inverse that allows for reconstruction of the low frequency content of the scattering kernel, up to quadratic error, from the nonlinear map. An iterative scheme is used to improve this error so that it is small when the high frequency content of the scattering kernel is small.