Medical Image Processing Group, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China.
IEEE Trans Biomed Eng. 2010 Oct;57(10):2564-7. doi: 10.1109/TBME.2010.2053538. Epub 2010 Jun 21.
Fluorescence molecular tomography has become a promising technique for in vivo small animal imaging and has many potential applications. Due to the ill-posed and the ill-conditioned nature of the problem, Tikhonov regularization is generally adopted to stabilize the solution. However, the result is usually over-smoothed. In this letter, the third-order simplified spherical harmonics approximation to radiative transfer equation is utilized to model the photon propagation within biological tissues. Considering the sparsity of the fluorescent sources, we replace Tikhonov method with an iteratively reweighted scheme. By dynamically updating the weight matrix, L1-norm regularization can be approximated, which can promote the sparsity of the solution. Simulation study shows that this method can preserve the sparsity of the fluorescent sources within heterogeneous medium, even with very limited measurement data.
荧光分子断层成像是一种很有前途的活体小动物成像技术，具有许多潜在的应用。由于问题的不适定性和病态性质，通常采用 Tikhonov 正则化来稳定解。然而，结果通常会过度平滑。在这封信中，利用简化的三阶球谐函数逼近辐射传输方程来模拟生物组织内的光子传播。考虑到荧光源的稀疏性，我们用迭代重加权方案代替 Tikhonov 方法。通过动态更新权重矩阵，可以逼近 L1-范数正则化，从而促进解的稀疏性。仿真研究表明，该方法即使在有限的测量数据下，也能保持异质介质中荧光源的稀疏性。
