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

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 Ricker 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.