基于X-ray图像重建算法研究及在集成电路领域的应用
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摘要
随着SMT组件的高密度化，在大规模集成电路制造组装过程中，实际生产中组装故障高达85%而现有的相关检测方法如人工目视检查自动光学检测等都只能对组件表面缺陷进行检测，对焊点在器件底面等不可视情况无能为力基于三维重建的缺陷检测在大规模集成电路领域的应用便是基于此背景诞生的，而国内在此方面的研究还处于空白阶段
论文以基于X-ray的三维重建为研究内容，重点研究了二维切片图像重建环节，提出了相关的重建模型及数值算法，并将文中的算法结合大规模集成电路领域的特点进行了研究，具体内容如下：
1)针对ART-TV算法迭代收敛速度缓慢的缺点，提出了基于多项式加速概念的P-TV新算法，并对算法中参数的取值进行了分析通过数值实验验证了算法的高效性，重建速度约提高了10倍另外，对实验过程中投影系数矩阵的获取和存储方法进行了改进，传统的投影系数矩阵通过建立射线源被测物体和探测屏的几何模型并求解获取，过程复杂耗时文中提出一种简单适用便于程序化操作的方法，并采用稀疏矩阵概念进行存储，极大地提高了实验的效率
2)采用一阶TV函数作为正则项重建图像会出现伪边缘现象和阶梯现象，而采用高阶TV函数又使得重建图像边缘模糊化文中基于二者的优点提出两种混合优化目标函数，Multi-TV函数和Mix-TV函数，并分别针对各向同性TV定义和各向异性TV定义对这两种目标函数进行了讨论最后采用文中提出的基于多项式加速框架的P-Multi-TV算法和P-Mix-TV算法进行图像重建，得到了良好的重建质量
3)在全变差函数空间内，分别讨论了ROF模型和高阶全变分模型的优劣，文中结合ROF模型和高阶模型的优点，提出一种基于全变分的混合模型采用基于Bregman距离的Split Bregman算法对混合模型进行求解，并从理论上证明了算法收敛性通过与多种算法的对比实验，验证了算法具有较好的自适应性和鲁棒性
4)针对集成电路领域中图像的特点，简化了重建模型，并给出了相应的求解算法最后通过实验验证了算法在保证图像重建质量的前提下极大的提高了重建速度，更加适合实时检测的需要
With the SMT components' high density, the actual assembly faults are up to85%duringthe LSI manufacturing and assembly process.However, the existing detection methods such asartificial visual inspection, automated optical inspection are only useful for surface defects.These methods are helpless for the situation when the welding spot defects are on the bottomof the device and other invisible situations.Under such background; defect detection based onthree-dimensional reconstruction is applied in the LSI field. But up till now, domestic researchon this area is still a blank stage.
In this thesis, the main research content is three-dimensional reconstruction based on theX-ray. We focus on the step of slice image reconstruction, proposed several reconstructionmodels and corresponding numerical algorithms. Finally, we do some research combined thecharacteristics of the LSI field with the proposed algorithms in the thesis, as follows:
1) Because of the slowly converges of ART-TV iterative algorithm, we propose a newalgorithm called P-TV based on the concept of polynomial acceleration, and then,we make an analysis about the parameter values. Numerical experiments resultsshow that the new algorithm is efficient and reconstruction speed is about10timeshigher than ART-TV algorithm. In addition, the acquisition and storage of theprojection matrix method is improved during the experiment. Conventional methodis so complex and time consuming. So, a new simple method is proposed in thepaper and it is easy to programming for acquiring the projection matrix, and then,the concept of sparse matrix is applied to storing the projection matrix, whichgreatly improves the efficiency of the experiment.
2) There are some ladder phenomena and pseudo-edge phenomena when we appliedfirst-order TV function as the regularization. However, it will lead to blurred edgeswhen we applied higher-order TV function as the egularization. The paper proposestwo mixing optimization objective function based on the advantages of first-orderTV and higher-order TV. That is Multi-TV function and Mix-TV function. Then, wemake discussion about isotropic TV and anisotropic TV definition. Finally, we makeexperiments with P-Multi-TV algorithm and P-Mix-TV algorithm under polynomialacceleration framework for image reconstruction, and we get a good reconstructionquality.
3) We make a discussion about advantages and disadvantages of ROF model andhigher totalvariation model based on the definition of the total variation function space. This thesis presents a hybrid model based on total variation which combineshigher totalvariation model and ROF model. Verified by experiments, this newmodel and solution strategies have great contribution for reconstruction quality. Weapplied Split Bregman algorithm for solving the new model and show a detailedderivation about algorithm, and then, make a point of convergence of the algorithm.Finally, new algorithm shows great adaptability and robustness according tonumerical experiments compared to other algorithms.
4) For the characteristics of the image in the field of integrated circuits, we prompt animplified reconstruction model and give the corresponding solution algorithm.Algorithm greatly improves the speed of reconstruction whileguarantees the qualityof the reconstruction image.So, the algorithm is verified more suitable for real-timedetection needs according to experiment analysis.
论文以基于X-ray的三维重建为研究内容，重点研究了二维切片图像重建环节，提出了相关的重建模型及数值算法，并将文中的算法结合大规模集成电路领域的特点进行了研究，具体内容如下：
1)针对ART-TV算法迭代收敛速度缓慢的缺点，提出了基于多项式加速概念的P-TV新算法，并对算法中参数的取值进行了分析通过数值实验验证了算法的高效性，重建速度约提高了10倍另外，对实验过程中投影系数矩阵的获取和存储方法进行了改进，传统的投影系数矩阵通过建立射线源被测物体和探测屏的几何模型并求解获取，过程复杂耗时文中提出一种简单适用便于程序化操作的方法，并采用稀疏矩阵概念进行存储，极大地提高了实验的效率
2)采用一阶TV函数作为正则项重建图像会出现伪边缘现象和阶梯现象，而采用高阶TV函数又使得重建图像边缘模糊化文中基于二者的优点提出两种混合优化目标函数，Multi-TV函数和Mix-TV函数，并分别针对各向同性TV定义和各向异性TV定义对这两种目标函数进行了讨论最后采用文中提出的基于多项式加速框架的P-Multi-TV算法和P-Mix-TV算法进行图像重建，得到了良好的重建质量
3)在全变差函数空间内，分别讨论了ROF模型和高阶全变分模型的优劣，文中结合ROF模型和高阶模型的优点，提出一种基于全变分的混合模型采用基于Bregman距离的Split Bregman算法对混合模型进行求解，并从理论上证明了算法收敛性通过与多种算法的对比实验，验证了算法具有较好的自适应性和鲁棒性
4)针对集成电路领域中图像的特点，简化了重建模型，并给出了相应的求解算法最后通过实验验证了算法在保证图像重建质量的前提下极大的提高了重建速度，更加适合实时检测的需要
With the SMT components' high density, the actual assembly faults are up to85%duringthe LSI manufacturing and assembly process.However, the existing detection methods such asartificial visual inspection, automated optical inspection are only useful for surface defects.These methods are helpless for the situation when the welding spot defects are on the bottomof the device and other invisible situations.Under such background; defect detection based onthree-dimensional reconstruction is applied in the LSI field. But up till now, domestic researchon this area is still a blank stage.
In this thesis, the main research content is three-dimensional reconstruction based on theX-ray. We focus on the step of slice image reconstruction, proposed several reconstructionmodels and corresponding numerical algorithms. Finally, we do some research combined thecharacteristics of the LSI field with the proposed algorithms in the thesis, as follows:
1) Because of the slowly converges of ART-TV iterative algorithm, we propose a newalgorithm called P-TV based on the concept of polynomial acceleration, and then,we make an analysis about the parameter values. Numerical experiments resultsshow that the new algorithm is efficient and reconstruction speed is about10timeshigher than ART-TV algorithm. In addition, the acquisition and storage of theprojection matrix method is improved during the experiment. Conventional methodis so complex and time consuming. So, a new simple method is proposed in thepaper and it is easy to programming for acquiring the projection matrix, and then,the concept of sparse matrix is applied to storing the projection matrix, whichgreatly improves the efficiency of the experiment.
2) There are some ladder phenomena and pseudo-edge phenomena when we appliedfirst-order TV function as the regularization. However, it will lead to blurred edgeswhen we applied higher-order TV function as the egularization. The paper proposestwo mixing optimization objective function based on the advantages of first-orderTV and higher-order TV. That is Multi-TV function and Mix-TV function. Then, wemake discussion about isotropic TV and anisotropic TV definition. Finally, we makeexperiments with P-Multi-TV algorithm and P-Mix-TV algorithm under polynomialacceleration framework for image reconstruction, and we get a good reconstructionquality.
3) We make a discussion about advantages and disadvantages of ROF model andhigher totalvariation model based on the definition of the total variation function space. This thesis presents a hybrid model based on total variation which combineshigher totalvariation model and ROF model. Verified by experiments, this newmodel and solution strategies have great contribution for reconstruction quality. Weapplied Split Bregman algorithm for solving the new model and show a detailedderivation about algorithm, and then, make a point of convergence of the algorithm.Finally, new algorithm shows great adaptability and robustness according tonumerical experiments compared to other algorithms.
4) For the characteristics of the image in the field of integrated circuits, we prompt animplified reconstruction model and give the corresponding solution algorithm.Algorithm greatly improves the speed of reconstruction whileguarantees the qualityof the reconstruction image.So, the algorithm is verified more suitable for real-timedetection needs according to experiment analysis.
引文
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