| 陈赞,滕召翼,冯远静.基于Q空间轨迹成像具有半正定约束的扩散偏度成像[J].高技术通讯(中文),2026,36(1):15~28 |
| 基于Q空间轨迹成像具有半正定约束的扩散偏度成像 |
| Diffusion skewness imaging based on Q-space trajectory imaging with semidefinite constraints |
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| DOI：10. 3772 / j. issn. 1002 - 0470. 2026. 01. 002 |
| 中文关键词: 扩散磁共振成像； Q空间轨迹成像； 偏度张量； 半正定规划； 微观分数各向异性 |
| 英文关键词: diffusion magnetic resonance imaging(MRI), Q-space trajectory imaging, skewness tensor, semidefinite programming, microscopic fractional anisotropy |
| 基金项目: |
| 作者 | 单位 | | 陈赞 | （浙江工业大学信息工程学院杭州 310023） | | 滕召翼 | | | 冯远静 | |
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| 摘要点击次数: 24 |
| 全文下载次数: 17 |
| 中文摘要: |
| Q空间轨迹成像（Q-space trajectory imaging，QTI）旨在通过扩散张量分布（diffusion tensor distribution，DTD）模型对微观组织结构进行探索，从而提高微环境中组织结构的区分度。在这项工作中，考虑到被测信号的不规则性，单靠低阶项拟合会丢弃较多的有用信息，为丰富结构信息并提高指标精确性，引入了具有更高阶数的偏度张量。针对拓展后的模型，为保证结果的合理性，提出了扩散张量、协方差张量和偏度张量应满足的3个约束条件，并证明其必要性。为便于约束条件加入到计算中，使用半正定规划（semidefinite programming，SDP）对问题进行求解。此外，本文还引入一个滤波函数，对微观组织结构进行表征。最后，在预处理后的数据集中加入高斯噪声，研究噪声对所提方法的影响。通过对约束条件必要性的讨论可以发现，若不对模型执行严格非负性，最终得到的结果会出现较大的误差，从而影响组织结构的分析。相应地，本文对高斯噪声可能带来的影响进行了测试，从实验结果可以看出，噪声的出现会给结果带来一定的误差，且误差不可以忽略。 |
| 英文摘要: |
| Q-space trajectory imaging (QTI) aims to improve the differentiation of tissue structures in microenvironments by exploring microstructures through diffusion tensor distribution (DTD) models. In this work, low-order term fitting will discard sustantial useful information when considering irregularity of the measured signals. To enrich structural details and improve the accuracy of the indicators, skewness tensors of higher orders are introduced. For the extended model, to ensure the rationality of the results, this article proposes three constraints that the mean diffusion tensor, the covariance tensor and the skewness tensor should satisfy.It also demonstrate their necessity. To facilitate the constraints to be added to the computation, semidefinite programming (SDP) is used to solve the problem. In addition, this article also introduces a filtering function to characterize the microstructure. Finally, Gaussian noise is added to the preprocessed dataset to investigate the effect of noise on our method. By discussing the necessity of the constraints, it can be found that if we do not enforce strict nonnegativity on the model, the results obtained from the final computation may show large errors, which can affect our analysis of the organizational structure. Accordingly, this article tested the effect of noise, and the experimental results show that the appearance of noise will bring a certain error to the results, which is not ignorable. |
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