X射线图像分析中的MCMC-Bayesian理论与计算方法研究

Aiming at the problems of high-energy X-ray such as imaging blur and serious noise, the efficient methods of X-ray image reconstruction and data analysis based on the MCMC-Bayesian method are studied. Firstly, the X-ray imaging of the parallel beam projection under the ideal condition and the cone beam projection for the practical application are modeled respectively, and the low-rank prior and multiscale iteration are combined for blind deconvolution of X-ray image. Then the Bayesian modeling methods for X-ray image reconstruction under two beam projections are studied respectively. For the reconstruction model with parallel beam projection, a Gibbs sampling method combining priori constraints and boundary enhancement is proposed to obtain the optimal estimation of the reconstructed image; for the reconstruction model with cone beam projection, a PMCMC algorithm based on Gibbs-based M-H sampling strategy is proposed to solve the high-dimensional nonlinear parametric space model. Finally, the NSCT domain modulus maximum algorithm based on super-resolution reconstruction is proposed to realize the object boundary of sub-pixel precise detection, and estimate the density distribution of the object. Our project is a novel and useful attempt to solve the nonlinear high-dimensional inversion problem. It will further improve the accuracy of the primary diagnostic object interface and density measurement of nuclear weapons, and plays an important role in promoting and developing the national defense and scientific research of our country.

针对高能X射线成像模糊、噪声强等问题，研究基于MCMC-Bayesian的X射线图像重建和数据分析的高效方法。首先，分别对理想状态下的平行束和实际应用中的锥形束投影下的X射线成像进行建模，结合低秩先验和多尺度迭代实现X射线图像的盲去卷积。然后分别研究两种光束投影下的X射线图像重建的贝叶斯建模方法。对于平行束投影下的重建模型，提出结合先验约束和边界增强的Gibbs抽样方法，以获得重建图像的最佳估计；对于锥形束投影下的重建模型，提出基于Gibbs范围内的M-H抽样策略的PMCMC算法，对高维的参数空间非线性模型进行求解。最后，提出基于超分辨率重建的NSCT域模极大值算法实现客体界面的亚像素级精确检测，并估计客体的密度分布参量。本项目的研究在求解非线性高维反演问题上是一种新颖的有益尝试，将进一步提高核武器初级诊断客体界面和密度测量的精度，对我国国防建设和科研水平的提升都具有重要的研究意义。

高能闪光X射线照相技术是诊断武器内部物理与几何特征的主要手段，具有成像速度快、穿透能力强和无损检测等优点。由于成像过程复杂、图像质量差，X射线图像目标界面和密度的测量是科学与工程界的难题之一。本项目旨在提高图像重建质量，深入研究X射线图像复原、线性与非线性重建、边缘检测以及目标密度测量等方法。.首先对X射线图像的区域极值和模糊核的稀疏性进行约束，结合不连续核元素的抑制估计出系统模糊核；结合二次和稀疏诱导范数构建复原模型，提出具备闭合解、非负约束的MCMC算法高效采样目标参数的后验分布，并利用“暖启动”技术逐步优化以实现图像复原；研究平行束投影下的线性重建模型，设计两级约束框架并考虑后验分布的变量分裂形式，采用一阶截断CG优化器的高效MCMC算法近似目标参数的后验分布，获得线性重建图像的最佳估计；针对模糊影响下的非线性重建问题，引入基于弱信息先验的超参数构建非线性分层贝叶斯模型，通过加速求解随机扰动的优化问题进行采样，结合雅可比矩阵投影约束求解过程，并设计目标参数的提议分布以减小样本统计偏差，在最小方差准则下融合线性与非线性模型的样本值，实现非线性重建模型的精准求解；最后，提出基于自适应各向异性因子和多尺度融合的边缘检测算法得到目标的边缘信息，通过标记块多指数拟合扣除质量系数，对面密度与透射率图像分别进行线性重建与非线性重建，完成目标密度的准确测量。.本项目实现了目标的高精度界面检测与密度重建，对目标界面的测量精度高于92%，对目标密度重建结果的相对误差低于6.80%。所提线性重建算法将非线性问题简化为线性问题，保证了计算效率与重建精度，经复原后可进一步提高目标界面与密度测量精度；所提非线性重建算法结合估计的模糊核，拥有更高的重建精度。本项目的研究在求解高维反演问题上是一种新颖的有益尝试，将进一步提高核武器初级诊断客体界面和密度测量的精度，对我国国防建设和科研水平的提升都具有重要的研究意义。.

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