Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, 100084, China.
Med Biol Eng Comput. 2013 Aug;51(8):849-58. doi: 10.1007/s11517-013-1054-5. Epub 2013 Mar 16.
The high degree of absorption and scattering of photons propagating through biological tissues makes fluorescence molecular tomography (FMT) reconstruction a severe ill-posed problem and the reconstructed result is susceptible to noise in the measurements. To obtain a reasonable solution, Tikhonov regularization (TR) is generally employed to solve the inverse problem of FMT. However, with a fixed regularization parameter, the Tikhonov solutions suffer from low resolution. In this work, an adaptive Tikhonov regularization (ATR) method is presented. Considering that large regularization parameters can smoothen the solution with low spatial resolution, while small regularization parameters can sharpen the solution with high level of noise, the ATR method adaptively updates the spatially varying regularization parameters during the iteration process and uses them to penalize the solutions. The ATR method can adequately sharpen the feasible region with fluorescent probes and smoothen the region without fluorescent probes resorting to no complementary priori information. Phantom experiments are performed to verify the feasibility of the proposed method. The results demonstrate that the proposed method can improve the spatial resolution and reduce the noise of FMT reconstruction at the same time.
生物组织中传播的光子的高吸收率和散射率使得荧光分子断层成像（FMT）重建成为一个严重的不适定问题，并且重建结果容易受到测量噪声的影响。为了得到一个合理的解，通常采用 Tikhonov 正则化（TR）来解决 FMT 的反问题。然而，对于固定的正则化参数，Tikhonov 解的分辨率较低。在这项工作中，提出了一种自适应 Tikhonov 正则化（ATR）方法。考虑到较大的正则化参数可以用低空间分辨率平滑解，而较小的正则化参数可以用高噪声水平锐化解，ATR 方法在迭代过程中自适应地更新空间变化的正则化参数，并使用它们来惩罚解。ATR 方法可以充分锐化有荧光探针的可行区域，并平滑没有荧光探针的区域，而无需使用互补的先验信息。通过进行体模实验验证了所提出方法的可行性。结果表明，该方法可以在提高 FMT 重建的空间分辨率的同时降低噪声。
