基于压缩感知的生物发光断层成像重建方法研究
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摘要
生物发光断层成像（Bioluminescence Tomography，BLT）作为一种领先的光子影像技术，由于其本身成像信噪比相对较高，而且具有安全性和灵敏性等优点，近年来受到了学者的广泛关注。目前生物发光断层成像已开始应用于基因表达、肿瘤检测和药物研发等小动物实验和预临床实验。目前生物发光断层成像研究热点集中于前向模型求解和逆向光源重建两方面。由于BLT是早期成像，因此BLT光源在生物体内呈现稀疏分布，导致生物体表逃逸出的光子数较少，成像设备在体表采集到的光学信号比较弱。另外由于光子在生物体内传输过程的复杂性，生物发光断层成像的逆重建问题在数学上是一个严重病态的欠定线性方程求解问题，是一个具有挑战性的问题。本文基于压缩感知理论，利用BLT光源的稀疏特性，对逆重建问题展开研究，所取得的主要研究成果为：
1.针对l2正则化方法重建结果过于平滑的问题，提出了基于初始对偶内点法的生物发光断层成像重建方法。基于l2正则化方法的BLT重建方法，重建结果分布范围较大，远远超出光源本身大小，而且重建光源能量分布过于平滑。因此基于压缩感知理论，利用生物发光光源的稀疏分布特性，研究初始对偶内点法解决生物发光断层成像的光源重建问题。本方法将BLT光源重建问题从基于l1范数的稀疏正则化转化为求解极小化的线性规划问题，并采用初始对偶内点法得到极小化问题的初始对偶形式；然后引入对数障碍函数，通过Karush-Kuhn-Tucker条件得到初始对偶方程；最后采用牛顿法得到方程的最优解。仿真实验证明了该方法的准确性和有效性，同时在体实验说明了方法在预临床肿瘤早期检测应用中的可行性。
2.针对目前大部分BLT重建方法稀疏性不足的问题，提出了基于加权迭代收缩阈值方法的生物发光断层成像重建方法。一些数值计算研究表明，在某些情况下，基于l1范数的正则化方法稀疏性要小于基于lp(0 3.针对各种可能影响生物发光断层成像重建的因素，选用一组通用的测试条件来评价多种常用的正则化重建方法的性能，以期为相关研究者选择和设计重建算法时提供一个公平的参考。选用的测试条件包括实验可行区、测量噪声(0%-50%)、光学参数、组织特异性、光源位置，以及单、双光源仿真实验和在体实验。基于一系列测试实验结果，我们发现基于lp(0 4.针对l1正则化在估值时经常引入额外偏差的问题，以及为了更好的逼近稀疏目标函数的l0正则子，提出了基于l1/2范数的加权内点法求解生物发光断层成像重建问题。在实际应用中，l1正则子的稀疏性通常要小于l0正则子，无法获得最好的稀疏重建效果；而l0正则子为NP难问题，无法直接求解，因此为了寻找比l1正则化方法更稀疏的求解方法，我们将用于求解极小化问题的lp(0In recent years, bioluminescence tomography (BLT) has been widely studied as apromising optical molecular imaging technique due to its significant advantages in highspecificity, sensitivity, safety and cost effectiveness high signal-to-noise ratio (SNR).Bioluminescence tomography has been applied in the animal experiments andpreclinical trials of gene expression, tumor detection and drug development, etc. Nowthe research of bioluminescence tomography focus on the forward model and theinverse reconstruction of the light source. As an early imaging modality, the source ofBLT has a sparse distribution and the optical signals obtained by the imaging equipmentfrom the surface of the animal are weak. Meanwhile because the transmission of photonis complex, the inverse reconstruction of the BLT light source is a severely ill-posedproblem as an underdetermined linear equation in mathematics. Based on thecompressed sensing theory and the sparsity of bioluminescent source distribution, thedissertation conducts the inverse reconstruction problem. The author’s majorcontributions are outlined as follows:
1. A three-dimensional bioluminescence tomography reconstruction algorithm isproposed based on primal-dual interior-point method. In order to reduce the severelyill-posedness of the BLT inverse problem, we propose a primal-dual interior-point(PDIP) method based on the compressed sensing theory and the sparsity ofbioluminescent source distribution. The PDIP method takes the l1norm problem as aminimization problem of linear programming. In order to obtain the optimal solution ofthe minimization problem, the Karush-Kuhn-Tucker condition is used to restrain thesolving process. Using the Newton method, we obtain the optimal solution to theprimal-dual equation. Reconstruction results on numerical simulation validate theaccuracy and effectiveness of the proposed method. Then in vivo mouse experimentvalidate the feasibility of the proposed method in early detection of clinicaloncology.
2. A three-dimensional bioluminescence tomography reconstruction algorithm isproposed based on weighted iterative shrinkage/thresholding algorithm (WISTA). Insome computational studies, l1regularization methods are often less sparse than lp(0 3. A comparison of six regularization methods is conducted through a series ofexperiments to study various conditions that affect the inverse BLT reconstruction. Theregularization methods have become the mainstream strategy to obtain the optimalsolution of the BLT inverse problem. But there is no generally accepted method whichcan be suitable for all of the reconstruction cases. We intend to fill the gap in theexisting studies to systematically benchmark the performance of thelp-regularization-based BLT reconstruction algorithms. In order to investigate theresponses of these algorithms to the permissible source region, measurement noise,optical properties and tissue specificity, we conduct a series of single source numericalphantom experiments. Then, the double sources numerical phantom experiment and thein vivo mouse experiment are carried out to further test their performances. For mostexperiments, the lp(0 4. A three-dimensional bioluminescence tomography reconstruction algorithm isproposed based on weighted interior-point algorithm (WIPA). In recent years, many l1regularization methods have been researched for various of inverse reconstructionproblem. However, the sparse property of the l1regularizer is often less than that of l0regularizer in many practical applications. In order to find more sparse solutions thanthe l1regularizer, many lp(0
1.针对l2正则化方法重建结果过于平滑的问题，提出了基于初始对偶内点法的生物发光断层成像重建方法。基于l2正则化方法的BLT重建方法，重建结果分布范围较大，远远超出光源本身大小，而且重建光源能量分布过于平滑。因此基于压缩感知理论，利用生物发光光源的稀疏分布特性，研究初始对偶内点法解决生物发光断层成像的光源重建问题。本方法将BLT光源重建问题从基于l1范数的稀疏正则化转化为求解极小化的线性规划问题，并采用初始对偶内点法得到极小化问题的初始对偶形式；然后引入对数障碍函数，通过Karush-Kuhn-Tucker条件得到初始对偶方程；最后采用牛顿法得到方程的最优解。仿真实验证明了该方法的准确性和有效性，同时在体实验说明了方法在预临床肿瘤早期检测应用中的可行性。
2.针对目前大部分BLT重建方法稀疏性不足的问题，提出了基于加权迭代收缩阈值方法的生物发光断层成像重建方法。一些数值计算研究表明，在某些情况下，基于l1范数的正则化方法稀疏性要小于基于lp(0
1. A three-dimensional bioluminescence tomography reconstruction algorithm isproposed based on primal-dual interior-point method. In order to reduce the severelyill-posedness of the BLT inverse problem, we propose a primal-dual interior-point(PDIP) method based on the compressed sensing theory and the sparsity ofbioluminescent source distribution. The PDIP method takes the l1norm problem as aminimization problem of linear programming. In order to obtain the optimal solution ofthe minimization problem, the Karush-Kuhn-Tucker condition is used to restrain thesolving process. Using the Newton method, we obtain the optimal solution to theprimal-dual equation. Reconstruction results on numerical simulation validate theaccuracy and effectiveness of the proposed method. Then in vivo mouse experimentvalidate the feasibility of the proposed method in early detection of clinicaloncology.
2. A three-dimensional bioluminescence tomography reconstruction algorithm isproposed based on weighted iterative shrinkage/thresholding algorithm (WISTA). Insome computational studies, l1regularization methods are often less sparse than lp(0
引文
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