LAUSR

To reduce the redundancy of nuclear magnetic resonance (NMR) echo data, kernel principal component analysis (KPCA) is used in the compression. The algorithm of data compression using KPCA is introduced in detail, and the specific calculation process is given. Four commonly used kernel functions are selected: Gaussian kernel, linear kernel, polynomial kernel, and exponential kernel. The compression effect of KPCA based on these four kernel functions on the NMR echo data obtained from complex pore structure formation is compared and analyzed. The study found that: Principal component analysis (PCA) is not suitable for the compression of NMR echo data obtained from the formation with complex pore structure. Compared with PCA, KPCA based on all the four kernels has obvious advantages in computational efficiency. The compression capabilities of KPCA based on Gaussian kernel and exponential kernel are all lower than PCA. The compression capability (CA) of KPCA based on linear kernel is equivalent to PCA. KPCA based on polynomial kernel, when the kernel parameter $\sigma \ge 2$ , its CA is higher than PCA. The compression accuracy of KPCA based on Gaussian kernel, linear kernel, and exponential kernel is stable in the formations with complex pore structure. KPCA based on polynomial kernel is sensitive to the kernel parameter, only when the kernel parameter $\sigma =5$ , the optimal compression accuracy can be obtained. At this time, the optimal compression effect is obtained in the complex pore formation.