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基于L1正则化稀疏约束的激发荧光断层重建方法研究
叶津佐
学位类型工学博士
导师田捷
2017-05-30
学位授予单位中国科学院研究生院
学位授予地点北京
关键词光学分子影像 激发荧光断层重建 L1范数正则化 非单调谱投影梯度方法 交替方向优化方法 稀疏度自适应
摘要光学分子影像技术是一种融合信息科学、数学以及生物医学的多学科交叉前沿成像技术,它的出现和应用,推动了医学影像的快速发展。在光学分子影像技术中,研究者将荧光标记物作为示踪剂注入生物体内,并使用影像学方法观测生物体内的肿瘤位置和生长发展情况等特征。光学分子影像技术对传统医学影像技术在功能和应用层面进行了有力的拓展,能够将肿瘤在生物体内的生长活动、药物在生物体内的代谢过程、肿瘤分子对治疗药物的表达过程进行可视化成像,从而实现在细胞、分子水平上对生物有机体内的生理、病理过程进行连续、动态的观测。激发荧光三维断层成像技术是光学分子影像技术中的一种重要模态,能够对生物体内标靶肿瘤的荧光分子探针(即荧光光源)的三维分布进行准确重建,从而提供一种对生物体中肿瘤位置和大小进行精确观测的手段,该技术是当前光学分子影像技术研究中的一大热点。
激发荧光成像的三维断层重建是通过光子在生物组织中传播的数学模型来反演计算和求解生物体内荧光光源三维分布的一种方法。由于激发荧光断层重建问题具有高度不适定性、病态性和计算规模大等难点,因此在重建精度、速度和鲁棒性方面存在很大的挑战。本文针对如何提高激发荧光断层重建的精度、速度和鲁棒性等问题,开展基于L1正则化稀疏约束的激发荧光断层重建方法研究,利用激发荧光断层成像的稀疏先验特性以及L1范数对数学模型最优解的稀疏促进作用,提出了三种新的重建方法,从精度、速度和鲁棒性三个方面提升了重建的性能。本文的主要工作和贡献如下:
  1. 提出了一种基于非单调谱投影梯度的激发荧光断层重建方法,实现对小鼠体内肿瘤位置的精确重建,并大幅度提升了重建的速度。非单调谱投影梯度方法是一种下降迭代类方法,它利用Barzilai-Borwein步长对迭代步长进行初始化,同时使用非单调线性搜索策略来确定算法的更新方向,并动态评估迭代步长的合理性,保证重建方法收敛到全局最优。同时,该方法利用谱投影梯度算子在每一步迭代中计算新的评估解,并结合L1正则化来保证重建结果的稀疏性。对该重建方法进行验证的数值仿真实验和在体实验的结果均表明,该方法比传统的重建方法具有更高的重建精度和更好的鲁棒性,而在重建效率方面则比传统重建方法提升了十倍。
  2. 提出了一种基于变量分裂思想和交替方向优化策略的激发荧光断层重建方法。激发荧光断层重建问题的稀疏求解可化简为一个加上L1范数正则化项的无约束优化问题,该重建方法从变量分裂的视角将需重建求解的无约束优化问题转换为等价的约束优化问题,通过求解与原问题等价的约束优化问题来完成重建。将无约束优化问题转换为约束优化问题的过程中,待求解变量由单个变量分裂变为两个变量。因此该重建方法使用交替方向优化策略来交替求解两个未知变量,处理双变量的迭代优化,使它们同步收敛到重建问题的最优解。该重建方法的优点是,求解转换后的等价问题变得简单,只需很少的迭代步数就能使其收敛到全局最优。数值仿真实验和在体实验证实该方法与传统的重建方法相比,收敛速度更快,同时也具有更高的重建精度和更好的鲁棒性。
  3. 提出了一种基于稀疏度自适应子空间追踪的激发荧光断层重建方法,提升了重建方法的普适性。该方法将基于L1范数正则化约束的激发荧光断层重建问题看作是一个基追踪问题,使用一个稀疏度因子来度量重建问题的稀疏性。传统基于基追踪问题的重建方法通常需要提前设定稀疏度因子,但在实际激发荧光断层成像中,不同问题的稀疏性存在差异,因而提前设定稀疏度因子的方法具有人为主观性,容易加大重建的误差。本文提出的稀疏度自适应子空间追踪重建方法则使用一维线性搜索策略在每一步迭代中自适应地评估稀疏度因子的合理性并更新稀疏度因子的大小,避免了提前设定稀疏度因子的弊端。此外,该重建方法还运用子空间投影和相关性最大化策略来简化原始重建问题的规模,并结合稀疏度因子构建重建问题的支撑集。数值仿真实验表明该方法针对具有不同稀疏度的重建问题都具有较高的重建精度,对测量数据中存在的噪声也具有较强的去除能力。在体实验的结果表明,该重建方法也具有良好的推广性。
其他摘要Optical molecular imaging is a fusion technology of information science, mathematics and biomedical imaging, its application has promote the rapid development of medical imaging. In optical molecular imaging, researchers injected the fluorescent marker as a tracer into the organism and used imaging technology to observe the location of tumors in the organism. Optical molecular imaging has expand the function and application for traditional medical imaging technology. It can visualize the growth activity of the tumor, the metabolic process of the drug and the expression process of the tumor molecule to the therapeutic drug, thus making the dynamic observation of the physiological and pathological processes possible in the small animals at the cell and molecular level. Fluorescence molecular tomography (FMT) is an important modality in optical molecular imaging technology that enables accurate reconstruction of the three-dimensional distribution of fluorescent molecular probes (i.e. fluorescent sources) in target tumors in vivo, thus providing a means of accurately observing the location and size of tumors in living organisms. FMT has become a hot spot in the research area of optical molecular imaging.
FMT reconstruction is a means of reconstruction the three-dimensional distribution of fluorescent sources in vivo by mathematical model of photon propagation in biological tissue. Due to the high ill-posedness, ill-condition and computational cost, FMT faces various challenges in accuracy, efficiency and robustness. In this thesis, we focus on improving the accuracy, efficiency and robustness of FMT, and carry out the research of FMT reconstruction based on L1 regularization sparse constraints. Three kinds of new reconstruction methods are proposed by us, which enhance the performance of reconstruction from three aspects: precision, speed and robustness. The main work of this thesis are listed as follows:
  1. We propose a method based on nonmonotone spectral projection gradient to reconstruct the tumor in mice and greatly increase the efficiency of FMT imaging. The method is a kind of descending iterative method. It uses the Barzilai-Borwein step to initialize the iterative step size while using a nonmonotone linear search strategy to determine the update direction and dynamically evaluate the iterative step size, thus ensuring the global convergence. Besides, this reconstruction method uses the spectral projection gradient operator to get the new solution in each step, and ensure the sparseness of the reconstruction result by using the L1 regularization. The outcome of phantom experiments and in vivo mouse experiments show that this method has higher reconstruction precision and robustness than the traditional FMT reconstruction methods. In terms of speed, this proposed method is much more faster than the traditional reconstruction method.
  2. We propose a method based on variable splitting strategy and alternating direction optimization for FMT reconstruction. The FMT inverse problem can be converted to an unconstrained optimization form with the regularization term of L1 norm. This reconstruction method transforms the original FMT problem to to an equivalent constraint optimization problem from the perspective of variable splitting, and then solve the equivalent optimization problem. In the process of converting the unconstrained optimization problem into a constraint form, the unknown to be solved is split into two variables. Therefore, the proposed reconstruction method uses the alternating direction optimization strategy to alternately solve two unknowns, and then get the reconstruction results of FMT inverse problem. The advantage of this reconstruction method is that solving the equivalent constrained optimization problem of the original problem becomes simple, and only a few iterative steps are needed to make it converge to global optimization. The outcom of the phantom experiments and mouse experiments show that the proposed method is faster than traditional reconstruction strategies, and also has higher reconstruction accuracy and robustness.
  3. We propose a method based on sparsity adaptive subspace pursuit for FMT reconstrucion. This method treats the problem of FMT with L1 norm regularization as a basis pursuit problem, and uses a sparsity factor to measure the sparseness of reconstruction problem. In traditional reconstruction methods based on basis pursuit, the sparsity factor is set in advance. However, in the FMT, the sparsity of different application is different, so the strategies of setting the sparsity factor in advance are human subjective, thus being easy to increase the error of result. Our algorithm uses a linear search strategy to adaptively evaluate the rationality of the sparsity factor and update its value in each iteration. This strategy can avoid the drawbacks of setting the sparsity factor in advance. In addition, the proposed reconstruction method also uses the subspace projection and correlation maximization strategy to simplify the original reconstruction problem, and constructs the support set of the problem with the help of sparsity factor. The outcome of the phantom experiments demonstrate that this algorithm has good reconstruction precision for FMT problems with different sparsities. The outcome of in vivo mouse experiments demonstrate that the proposed reconstruction algorithm also has a good generalization.
文献类型学位论文
条目标识符http://ir.ia.ac.cn/handle/173211/14842
专题毕业生_博士学位论文
作者单位中国科学院自动化研究所
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叶津佐. 基于L1正则化稀疏约束的激发荧光断层重建方法研究[D]. 北京. 中国科学院研究生院,2017.
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