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Frequency-domain optical tomographic image reconstruction algorithm with the simplified spherical harmonics (SP3) light propagation model

机译：具有简化球谐函数（SP3）光传播模型的频域光学层析图像重建算法

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We introduce here the finite volume formulation of the frequency-domain simplified spherical harmonics model with n-th order absorption coefficients (FD-SPN) that approximates the frequency-domain equation of radiative transfer (FD-ERT). We then present the FD-SPN based reconstruction algorithm that recovers absorption and scattering coefficients in biological tissue. The FD-SPN model with 3rd order absorption coefficient (i.e., FD-SP3) is used as a forward model to solve the inverse problem. The FD-SP3 is discretized with a node-centered finite volume scheme and solved with a restarted generalized minimum residual (GMRES) algorithm. The absorption and scattering coefficients are retrieved using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. Finally, the forward and inverse algorithms are evaluated using numerical phantoms with optical properties and size that mimic small-volume tissue such as finger joints and small animals.The forward results show that the FD-SP3 model approximates the FD-ERT (S12) solution within relatively high accuracy; the average error in the phase (<3.7%) and the amplitude (<7.1%) of the partial current at the boundary are reported. From the inverse results we find that the absorption and scattering coefficient maps are more accurately reconstructed with the SP3 model than those with the SP1 model. Therefore, this work shows that the FD-SP3 is an efficient model for optical tomographic imaging of small-volume media with non-diffuse properties both in terms of computational time and accuracy as it requires significantly lower CPU time than the FD-ERT (S12) and also it is more accurate than the FD-SP1.
机译：我们在这里介绍具有n阶吸收系数（FD-SPN）的频域简化球谐函数模型的有限体积公式，该模型近似于辐射传递的频域方程（FD-ERT）。然后，我们介绍基于FD-SPN的重建算法，该算法可恢复生物组织中的吸收和散射系数。具有3阶吸收系数的FD-SPN模型（即FD-SP3）被用作解决反问题的正向模型。 FD-SP3通过以节点为中心的有限体积方案离散化，并通过重新启动的广义最小残差（GMRES）算法进行求解。使用有限内存的Broyden-Fletcher-Goldfarb-Shanno（L-BFGS）算法检索吸收系数和散射系数。最后，使用具有模拟小手指，小动物等小体积组织的光学特性和大小的数值模型对正向和反向算法进行评估，正向结果表明FD-SP3模型近似于FD-ERT（S12）解决方案在相对较高的精度内；报告了边界处分电流的相位平均误差（<3.7％）和幅度（<7.1％）。从相反的结果，我们发现，使用SP3模型比使用SP1模型更准确地重建吸收和散射系数图。因此，这项工作表明FD-SP3是用于小体积介质的光学层析成像的有效模型，无论是在计算时间还是在准确性方面都具有非扩散特性，因为它需要比FD-ERT显着更少的CPU时间），并且比FD-SP1更准确。

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