Ricker子波核最小二乘支持向量回归滤波方法的稳健性研究

Robustness of least squares support vector regression filtering method with Ricker wavelet kernel

除了信噪比、有效子波畸变等,稳健性(Robustness)也是度量滤波方法效果的一个重要的物理量,它刻画了滤波系统应对异常点值的能力.一般用影响函数作为评价稳健性的工具.支持向量机方法已较成功地应用于信号与图像的滤波中,尤其Ricker子波核方法更适于地震勘探信号处理.通过考察Ricker子波核最小二乘支持向量回归(LS-SVR:least squares support vector regression)滤波方法的影响函数,可以证明该方法的稳健性较差,本文用加权方法改善该方法的稳健性.经过大量理论实验得到一种改进的权函数,使加权之后的方法具有比较理想的稳健性.进一步用这个权函数辅助的加权Ricker子波LS-SVR处理含噪的合成与实际地震记录,都得到较好的效果.由具有平方损失函数的LS-SVR信号处理系统的无界影响函数出发,本文所提出的权函数可以有效地应用于具有相似损失函数的处理过程,如消噪、信号检测、提高分辨率与预测等问题.

Besides the signal-to-noise ratio and distortion of desired wavelets, the robustness is also an important physical quantity to measure the effect of a filtering method. The robustness expresses how a filtering system to deal with outliers. Generally, the influence function is used as a tool to assess the robustness of methods. Support vector machine has been successfully applied to the filtering of signal or image. Especially, the Ricker wavelet kernel method is suitable for the seismic data processing. It can be proved by checking the influence function of least squares support vector regression （LS-SVR） with the Rieker wavelet kernel that the robustness of this method is less satisfactory. In this paper the weighted method is used to improve the robustness of LS-SVR with the Ricker wavelet kernel. From many theoretical experiments, we obtain an improved weight function. After using the weight function, the robustness is quite satisfactory. Furthermore, we apply the weighted LS-SVR with the Ricker wavelet kernel to process the noisy synthetic and real seismic data. As a result, the good performance is achieved. Considering that the influence function of the LS-SVR system with a square loss function is not bounded, the weight function proposed can be effectively applied to the processing with similar loss function such as denoising, signal detecting, resolution improving, predicting, etc.