A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium
A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium
复制标题
DOI：
10.1088/1361-6420/ab4d98
复制
发表时间：
2019-07
期刊：
影响因子：
2.1
通讯作者：
H. Fujiwara;K. Sadiq;A. Tamasan
中科院分区：
文献类型：
--
作者：
H. Fujiwara;K. Sadiq;A. Tamasan
我们重新讨论了在二维吸收和散射介质中的反源问题，并提出了一种直接重建方法，它不需要迭代求解的正问题，使用测量的辐射通量在边界处。衰减和散射系数是已知的，未知源是各向同性的。该方法基于序列值映射的Beltrami型方程的Cauchy问题，将Bukhgeim的原始思想从非散射介质推广到散射介质。我们证明了该方法的可行性，在数值实验中的散射是由二维Henyey-Greenstein内核与光学层析成像中有意义的参数建模。
We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a direct reconstruction method, which does not require iterative solvability of the forward problem, using measurements of the radiating flux at the boundary. The attenuation and scattering coefficients are known and the unknown source is isotropic. The approach is based on the Cauchy problem for a Beltrami-like equation for the sequence valued maps, and extends the original ideas of Bukhgeim from the non-scattering to the scattering media. We demonstrate the feasibility of the method in a numerical experiment in which the scattering is modeled by the two dimensional Henyey–Greenstein kernel with parameters meaningful in optical tomography.