漫射光学层析成像的逆Rytov级数
The inverse Rytov series for diffuse optical tomography
AI总结：
本文提出利用逆Rytov级数进行漫射光学层析成像的非线性重建，避免线性化，利用高阶项，并证明其收敛性与稳定性，结构类似逆Born级数。
摘要：
Rytov近似在近红外光谱学（包括漫射光学层析成像）中是已知的。在漫射光学层析成像中，Rytov近似通常比Born近似能给出更好的重建图像。尽管相关的逆问题是非线性的，但Rytov近似几乎总是伴随着非线性逆问题的线性化。在本文中，我们将利用逆Rytov级数发展非线性重建。由此，线性化不再是必需的，并且Rytov级数中的高阶项可用于重建。讨论了收敛性和稳定性。我们发现逆Rytov级数具有类似于逆Born级数的递归结构。
英文摘要：
The Rytov approximation is known in near-infrared spectroscopy including diffuse optical tomography. In diffuse optical tomography, the Rytov approximation often gives better reconstructed images than the Born approximation. Although related inverse problems are nonlinear, the Rytov approximation is almost always accompanied by the linearization of nonlinear inverse problems. In this paper, we will develop nonlinear reconstruction with the inverse Rytov series. By this, linearization is not necessary and higher order terms in the Rytov series can be used for reconstruction. The convergence and stability are discussed. We find that the inverse Rytov series has a recursive structure similar to the inverse Born series.
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