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	Study on Mercer condition extension of support vector regression based on Ricker wavelet kernel
	Deng Xiao-Ying ; Yang Ding-Hui ; Liu Tao ; Xie Jing
	2010-10-12 ; 2010-10-12
关键词	Support vector regression filtering based on the Ricker wavelet kernel Mercer condition extension Mixed-phase wavelet Strong random noise Signal-to-Noise Ratio (SNR) Mean Square Error (MSE) SEISMIC DATA NOISE ENHANCEMENT Geochemistry & Geophysics
中文摘要	Support vector regression (SVR) based on the Ricker wavelet kernel is a new filtering method for suppressing strong random noise in seismic records. The Mercer condition, which is the rule to determine a support vector admissible kernel, is used to discuss the validity of the Ricker wavelet kernel. By computing the minimum eigenvalues of kernel matrixest we find that there exist some small negative values in a wider region which have orders of magnitude 10(-13) similar to 10(-16), and also exist some small positive values which have orders of magnitude 10(-13) similar to 10(-15), Considering the same mechanism resulting in the positive and negative computational errors, we conclude that the Mercer condition can be moderately relaxed, that is, the kernel matrix can be not exactly positive semi-definite and close to positive semi-definite. In order to apply the SVR based on the Ricker wavelet kernel to practical applications, we compare the performances of our method, the wavelet transform-based method and adaptive Wiener filtering in detail, including the waveforms in the time domain, the amplitude spectrums in frequency domain, the SNRs before and after filtering and the MSEs. The results show that our method works better than the two other methods, which lays a foundation for practical applications of the SVR based on the Ricker wavelet kernel.
语种	中文 ; 中文
出版者	SCIENCE PRESS ; BEIJING ; 16 DONGHUANGCHENGGEN NORTH ST, BEIJING 100717, PEOPLES R CHINA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/81226]
专题	清华大学
推荐引用方式 GB/T 7714	Deng Xiao-Ying,Yang Ding-Hui,Liu Tao,et al. Study on Mercer condition extension of support vector regression based on Ricker wavelet kernel[J],2010, 2010.
APA	Deng Xiao-Ying,Yang Ding-Hui,Liu Tao,&Xie Jing.(2010).Study on Mercer condition extension of support vector regression based on Ricker wavelet kernel..
MLA	Deng Xiao-Ying,et al."Study on Mercer condition extension of support vector regression based on Ricker wavelet kernel".(2010).

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