Jia Mengyu, Jiang Jingying, Ma Wenjuan, Li Chenxi, Wang Shuang, Zhao Huijuan, Gao Feng
College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China.
Tianjin Medical University Cancer Institute & Hospital Tianjin, 300072, China.
Biomed Opt Express. 2017 Aug 31;8(9):4275-4293. doi: 10.1364/BOE.8.004275. eCollection 2017 Sep 1.
Image reconstruction in the most model-based biophotonic imaging modalities essentially poses an ill-posed nonlinear inverse problem, which has been effectively tackled in the diffusion-approximation-satisfied scenarios such as diffuse optical tomography. Nevertheless, a nonlinear implementation in high-resolution laminar optical tomography (LOT) is normally computationally-costly due to its strong dependency on a dense source-detector configuration and a physically-rigorous photon-transport model. To circumvent the adversity, we herein propose a practical nonlinear LOT approach to the absorption reconstruction. The scheme takes advantage of the numerical stability of the singular value decomposition (SVD) for the ill-posed linear inversion, and is accelerated by adopting an explicitly recursive strategy for the time-consuming repeated SVD inversion, which is based on a scaled expression of the sensitivity matrix. Experiments demonstrate that the proposed methodology can perform as well as the traditional nonlinear one, while the computation time of the former is merely 26.27% of the later on average.
在大多数基于模型的生物光子成像模态中，图像重建本质上是一个不适定的非线性逆问题，在诸如扩散光学层析成像等满足扩散近似的场景中，这个问题已经得到了有效解决。然而，在高分辨率层流光学层析成像（LOT）中，由于其强烈依赖密集的源探测器配置和物理上严格的光子传输模型，非线性实现通常计算成本很高。为了克服这一困难，我们在此提出一种用于吸收重建的实用非线性LOT方法。该方案利用奇异值分解（SVD）对不适定线性反演的数值稳定性，并通过采用基于灵敏度矩阵缩放表达式的耗时重复SVD反演的显式递归策略来加速。实验表明，所提出的方法与传统非线性方法性能相当，而前者的计算时间平均仅为后者的26.27%。
