生物发光断层成像中GPU加速及SDCA-ADMM优化重建算法的研究

发布时间：2018-08-08 20:37

【摘要】：生物发光断层成像(BLT)是通过荧光测量值对生物组织发光源进行重建,得到发光源的三维分布。BLT包括前向问题和逆问题两部分,在BLT前向问题中,需要解决的主要问题是光传输方式的精确建模以及快速求解。在几种光传输模型中,SPN模型实用性越来越高。但是在SPN模型中,由于N的上升,导致该模型的求解计算速度不断降低。而在逆问题过程中,由于使用大规模荧光数据有助于提高重建质量,但同时也会消耗大量的计算时间,因此针对大规模数据,需要进行快速重建方面的研究。本文分别对BLT前向的SPN模型中计算代价和后向问题中重建速度两方面进行了探索。主要工作包括:1)基于GPU的BLT前向问题的并行加速求解策略和实现。在有限元方法下,对BLT前向过程进行计算时间分析可得,刚度矩阵生成和线性方程组求解两部分在整个前向过程中耗时最高,且这两部分都非常适合并行化处理,因此将SPN模型作为光传输模型,结合GPU的并行处理能力提出一种基于GPU/CPU双平台的BLT前向问题加速策略。将前向过程分解成刚度矩阵生成、线性方程组求解、数据交换和条件判断四部分,其中将前两部分传输给GPU端进行加速运算,而后两部分交给CPU执行。数字鼠仿真实验验证了在本策略下,针对不同网格数量下的SP5模型的BLT前向整体加速比最高能达到20倍左右。2)针对大规模数据导致BLT重建耗时大的问题,提出了一种基于交替方向乘子法(ADMM)结合随机对偶坐标下降方法(SDCA)的BLT重建算法。通过SDCA方法随机选取某一坐标系方向将目标函数分解成多个子函数,使每个坐标下都有对应的子函数,然后再计算每个子函数的最优解,然后在迭代过程中按照最优解与真实值之间的接近程度依次选取对应坐标下的子函数,减少无关数据在迭代过程中的使用率,提升收敛速度,实现快速重建目的。数字鼠仿体实验和真实老鼠实验验证了在保证BLT重建图像精度的同时,重建速度提高了5倍左右。
[Abstract]:Bioluminescence tomography (BLT) is used to reconstruct the light source of biological tissue by fluorescence measurement, and the three-dimensional distribution of the light source. BLT includes two parts: forward problem and inverse problem. In the forward problem of BLT, The main problem to be solved is the accurate modeling and fast solution of optical transmission mode. Among several optical transmission models, the SPN model is becoming more and more practical. But in the SPN model, because of the rise of N, the calculation speed of the model is decreasing. In the inverse process, because the use of large-scale fluorescence data can improve the quality of reconstruction, but also consume a lot of computing time, so for large-scale data, we need to do research on rapid reconstruction. In this paper, the computational cost of the BLT forward SPN model and the reconstruction speed of the backward problem are explored respectively. The main work includes: 1) parallel accelerated solution strategy and implementation of BLT forward problem based on GPU. Under the finite element method, the computational time of BLT forward process can be analyzed. The stiffness matrix generation and the solution of linear equations are the most time-consuming in the whole forward process, and these two parts are very suitable for parallelization. Therefore, the SPN model is taken as the optical transmission model and the parallel processing ability of GPU is combined to propose a BLT forward problem acceleration strategy based on GPU/CPU dual platform. The forward process is decomposed into four parts: stiffness matrix generation, linear equation system solution, data exchange and condition judgment. The first two parts are transmitted to the GPU terminal for accelerated operation, and the latter two parts are handed over to CPU for execution. Digital rat simulation experiments show that under this strategy, the BLT forward overall acceleration ratio of SP5 model with different mesh number can reach 20 times. 2.) because of the large scale data, BLT reconstruction takes a lot of time. A BLT reconstruction algorithm based on alternating direction multiplier method (ADMM) and stochastic dual coordinate descent method (SDCA) is proposed. The objective function is decomposed into several subfunctions by the SDCA method in which the direction of a coordinate system is selected randomly, so that there are corresponding subfunctions in each coordinate system, and then the optimal solution of each subfunction is calculated. Then in the iterative process according to the approximate degree between the optimal solution and the real value the subfunctions in the corresponding coordinates are selected in order to reduce the utilization rate of independent data in the iterative process improve the convergence speed and achieve the purpose of fast reconstruction. The digital mouse body simulation experiment and the real mouse experiment show that the reconstruction speed is increased by about 5 times while the accuracy of BLT reconstruction image is guaranteed.
【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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