Ultrasound modulated bioluminescence tomography with a single optical measurement
Ultrasound modulated bioluminescence tomography with a single optical measurement
复制标题
DOI：
10.1088/1361-6420/abc8aa
复制
发表时间：
2020-08
期刊：
影响因子：
2.1
通讯作者：
Francis J. Chung;Tianyu Yang;Yang Yang-Yang
中科院分区：
文献类型：
--
作者：
Francis J. Chung;Tianyu Yang;Yang Yang-Yang
超声调制生物发光层析成像是一种成像方法，可以作为杂交源源问题配方。在通过辐射转移方程建模的光传播的制度中，以前解决此问题的方法需要大量的光学测量（Bal等人2016 Siam J.Math。Anal。481332）。在这里，我们为这个反问题提出了一种替代解决方案，该解决方案仅需要一个光学测量才能重建各向同性源。具体而言，我们分别基于Neumann Series和Fredholm理论得出了两个反转公式，并在充分条件下证明了它们的收敛性。在存在噪声的情况下，实现并实施了所得的数值算法，并实验以重建连续和不连续的来源。
Ultrasound modulated bioluminescence tomography is an imaging method which can be formulated as a hybrid inverse source problem. In the regime where light propagation is modeled by a radiative transfer equation, previous approaches to this problem require large numbers of optical measurements (Bal et al 2016 SIAM J. Math. Anal. 48 1332). Here we propose an alternative solution for this inverse problem which requires only a single optical measurement in order to reconstruct the isotropic source. Specifically, we derive two inversion formulae based on Neumann series and Fredholm theory respectively, and prove their convergence under sufficient conditions. The resulting numerical algorithms are implemented and experimented to reconstruct both continuous and discontinuous sources in the presence of noise.