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基于前向-后向分裂法的L1-L2范数正则化在荧光分子断层成像中的应用

L1-L2 norm regularization via forward-backward splitting for fluorescence molecular tomography.

作者信息

Zhang Heng, He Xiaowei, Yu Jingjing, He Xuelei, Guo Hongbo, Hou Yuqing

机构信息

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.

出版信息

Biomed Opt Express. 2021 Nov 29;12(12):7807-7825. doi: 10.1364/BOE.435932. eCollection 2021 Dec 1.

Abstract

Fluorescent molecular tomography (FMT) is a highly sensitive and noninvasive imaging approach for providing three-dimensional distribution of fluorescent marker probes. However, owing to its light scattering effect and the ill-posedness of inverse problems, it is challenging to develop an efficient reconstruction algorithm that can achieve the exact location and morphology of the fluorescence source. In this study, therefore, in order to satisfy the need for early tumor detection and improve the sparsity of solution, we proposed a novel - norm regularization via the forward-backward splitting method for enhancing the FMT reconstruction accuracy and the robustness. By fully considering the highly coherent nature of the system matrix of FMT, it operates by splitting the objective to be minimized into simpler functions, which are dealt with individually to obtain a sparser solution. An analytic solution of - norm proximal operators and a forward-backward splitting algorithm were employed to efficiently solve the nonconvex - norm minimization problem. Numerical simulations and an glioma mouse model experiment were conducted to evaluate the performance of our algorithm. The comparative results of these experiments demonstrated that the proposed algorithm obtained superior reconstruction performance in terms of spatial location, dual-source resolution, and practicability. It was believed that this study would promote the preclinical and clinical applications of FMT in early tumor detection.

摘要

荧光分子断层成像(FMT)是一种用于提供荧光标记探针三维分布的高灵敏度非侵入性成像方法。然而,由于其光散射效应和反问题的不适定性,开发一种能够精确实现荧光源位置和形态的高效重建算法具有挑战性。因此,在本研究中,为了满足早期肿瘤检测的需求并提高解的稀疏性,我们提出了一种通过前向-后向分裂方法的新型 - 范数正则化,以提高FMT重建的准确性和鲁棒性。通过充分考虑FMT系统矩阵的高度相干性质,该方法通过将要最小化的目标分解为更简单的函数来操作,这些函数分别处理以获得更稀疏的解。采用 - 范数近端算子的解析解和前向-后向分裂算法来有效解决非凸 - 范数最小化问题。进行了数值模拟和胶质瘤小鼠模型实验来评估我们算法的性能。这些实验的比较结果表明,所提出的算法在空间定位、双源分辨率和实用性方面获得了优异的重建性能。相信本研究将促进FMT在早期肿瘤检测中的临床前和临床应用。

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本文引用的文献

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