面向多投影数据的荧光分子断层成像快速重建方法研究

发布时间：2018-03-10 18:46

本文选题：分子影像　切入点：荧光分子断层成像　出处：《西北大学》2017年硕士论文　论文类型：学位论文

【摘要】：荧光分子断层成像作为一种重要的分子成像模态,在肿瘤检测、疾病治疗和药物研发方面得到了广泛应用。但由于光的强散射特性以及测量数据的不足,使得重建问题具有严重的病态性。为降低重建的病态性,得到鲁棒的重建结果,研究者通常采集多个投影角度的荧光数据进行重建。大规模的投影数据给重建带来了复杂的矩阵运算,使得计算复杂、耗时。本文围绕重建精度和重建效率,从矩阵维数约减的角度出发开展FMT重建算法研究。具体内容如下:采用多角度投影的数据进行重建需要较大的计算内存和耗费较长的计算时间。本文采用满足正交投影变换原理的主成分分析将原本繁琐复杂的数据集线性变换到维数相对较小的数据集上,然后利用降维后规模较小的数据集并且结合稀疏正则化算法进行重建。实验结果表明经过降维后重建时间缩短数10倍。基于流形学习和压缩感知理论,本文提出了结合局部保留投影和稀疏正则化的重建方法,该方法利用局部保留投影将表面荧光数据进行局部的线性特征抽取,得到的局部数据可以较为完整的包含整个数据的全局特征同时也很好的保留了原有数据的非线性结构。因为重建使用了规模较小的局部数据,所以加快了重建速度,同时还改善了目标的重建精度和聚集性。实验结果表明本方法在减少重建时间的同时还能改善目标的定位精度,具有很强的鲁棒性。提出基于线性近似回归和对偶增广拉格朗日的荧光分子断层成像。线性近似回归方法可以有效解决大规模矩阵特征提取,将原始的多投影数据进行处理得到新的子空间数据,然后采用基于对偶问题稀疏重建的增广拉格朗日方法进行三维重建得到重建结果。该方法能很好降低问题病态性,与传统重建方法相比,该方法特别适合矩阵条件数较差且矩阵规模较大的情形。数值仿真实验和真实小鼠实验验证了方法的鲁棒性和稳定性,重建速度也进一步加快。
[Abstract]:As an important molecular imaging mode, fluorescence molecular tomography has been widely used in tumor detection, disease treatment and drug development. In order to reduce the pathogenicity of reconstruction, the robust reconstruction results are obtained. Researchers usually collect fluorescence data from multiple projection angles for reconstruction. Large scale projection data bring complex matrix operation to reconstruction, making computation complex and time-consuming. This paper focuses on reconstruction accuracy and reconstruction efficiency. The research of FMT reconstruction algorithm is carried out from the angle of matrix dimension reduction. The main contents are as follows: the reconstruction of multi-angle projection data requires large computational memory and long computation time. The principal component analysis (PCA) of the principle of intersection projection transforms the original complicated data set into a data set with relatively small dimension. Then we use the smaller dimensionally reduced data set and the sparse regularization algorithm to reconstruct. The experimental results show that the reconstruction time is reduced by 10 times after dimensionality reduction. Based on manifold learning and compression perception theory, In this paper, a reconstruction method combining local preserving projection with sparse regularization is proposed, in which the local linear feature extraction of the surface fluorescence data is carried out by using the local preserving projection. The local data can contain the global features of the whole data completely, and it also preserves the nonlinear structure of the original data very well. Because the reconstruction uses smaller local data, it speeds up the reconstruction speed. The experimental results show that the proposed method not only reduces the reconstruction time but also improves the positioning accuracy of the target. The fluorescence molecular tomography based on linear approximate regression and dual augmented Lagrangian is proposed. The linear approximate regression method can effectively solve the large-scale matrix feature extraction. The original multi-projection data are processed to obtain the new subspace data, and then the augmented Lagrangian method based on the sparse reconstruction of dual problems is used to obtain the reconstruction results. This method can reduce the ill-condition of the problem very well. Compared with the traditional reconstruction method, this method is especially suitable for the case where the matrix condition number is poor and the matrix size is large. The robustness and stability of the method are verified by numerical simulation and real mouse experiments, and the reconstruction speed is further accelerated.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：R318;TP391.41

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