Abstract: The kernel function methods can discover the nonlinear distribution rules among the images of high precision prints. And the mining capacity is decided by the kernel function and its parameters. Selecting the kernel function is imminent to the development and application in kernel function theory. Based on the intelligent detection of prints, a new learning kernel method based on the optimization was presented for the industry of high precision printing to make the kernel function method to achieve optimal performance. Unlike the traditional calculation method, the kernel's parameter was continuously changing in kernel space, which meant that the learning scope expanded one dimension. The experimental results show that the iterative algorithm based on the theoretical analysis only needs ten iterations to get the statistical optimal kernel function and its parameters, and the recovery error of the kernel function is statistically minimum.

Key words: kernel method, optimization problem, defect detection, Kernel Principal Component Analysis (KPCA), image reconstruction

摘要： 核函数方法可挖掘出高精度快速印刷品图像间的非线性分布规律，而挖掘能力由所选择的核函数及其参数来决定。这两者的学习与选择同样是核函数理论继续发展与实际应用需要迫切解决的问题。针对印刷品智能检测这一特定背景，提出了一种新的基于优化问题的从具有动态参数的函数空间中学习核函数及参数的方法，以此来使核函数方法达到最优性能。与传统的计算方法不同之处在于其核函数空间中的核参数是连续变化的，这使学习的范围得到一个维度上的扩展。实验结果显示，结合理论分析的迭代算法仅需要10次迭代便可得到统计最优的核函数及参数，利用学习到的核函数计算的复原误差是统计最小的。

关键词: 核方法, 优化问题, 缺陷检测, 核主成分分析, 图像复原