The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China.
School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710119, China.
Comput Methods Programs Biomed. 2023 Jun;234:107503. doi: 10.1016/j.cmpb.2023.107503. Epub 2023 Mar 22.
Fluorescence molecular tomography (FMT) is a non-invasive molecular imaging modality that can be used to observe the three-dimensional distribution of fluorescent probes in vivo. FMT is a promising imaging technique in clinical and preclinical research that has attracted significant attention. Numerous regularization based reconstruction algorithms have been proposed. However, traditional algorithms that use the squared l-norm distance usually exaggerate the influence of noise and measurement and calculation errors, and their robustness cannot be guaranteed.
In this study, we propose a novel robust transformed l (TL1) metric that interpolates l and l norms through a nonnegative parameter α∈(0,+∞). The TL1 metric looks like the l-norm with p∈(0,1). These are markedly different because TL1 metric has two properties, boundedness and Lipschitz-continuity, which make the TL1 criterion suitable distance metric, particularly for robustness, owing to its stronger noise suppression. Subsequently, we apply the proposed metric to FMT and build a robust model to reduce the influence of noise. The nonconvexity of the proposed model made direct optimization difficult, and a continuous optimization method was developed to solve the model. The problem was converted into a difference in convex programming problem for the TL1 metric (DCATL1), and the corresponding algorithm converged linearly.
Various numerical simulations and in vivo bead-implanted mouse experiments were conducted to verify the performance of the proposed method. The experimental results show that the DCATL1 algorithm is more robust than the state-of-the-art approaches and achieves better source localization and morphology recovery.
The in vivo experiments showed that DCATL1 can be used to visualize the distribution of fluorescent probes inside biological tissues and promote preclinical application in small animals, demonstrating the feasibility and effectiveness of the proposed method.
荧光分子断层成像（FMT）是一种非侵入性的分子成像方式，可用于观察体内荧光探针的三维分布。FMT 是一种有前途的临床和临床前研究成像技术，引起了广泛关注。已经提出了许多基于正则化的重建算法。然而，传统的使用平方 l-norm 距离的算法通常会夸大噪声和测量及计算误差的影响，并且不能保证其稳健性。
在这项研究中，我们提出了一种新颖的鲁棒变换 l（TL1）度量标准，该标准通过非负参数α∈（0，+∞）对 l 和 l 范数进行插值。TL1 度量标准与 p∈（0，1）上的 l-范数看起来非常相似。这些度量标准有两个性质，有界性和 Lipschitz 连续性，这使得 TL1 标准适合作为距离度量标准，特别是在鲁棒性方面，因为它具有更强的噪声抑制能力。随后，我们将提出的度量标准应用于 FMT，并构建了一个鲁棒模型来降低噪声的影响。由于该模型的非凸性，直接优化比较困难，因此开发了一种连续优化方法来解决该模型。将该问题转换为 TL1 度量标准的差异凸规划问题（DCATL1），并相应的算法呈线性收敛。
进行了各种数值模拟和体内植入珠子的小鼠实验，以验证所提出方法的性能。实验结果表明，DCATL1 算法比最先进的方法更稳健，可实现更好的源定位和形态恢复。
体内实验表明，DCATL1 可用于可视化生物组织内荧光探针的分布，并促进小动物中的临床前应用，证明了所提出方法的可行性和有效性。
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