Least squares support vector regression filter

We combine the training and testing stages of support vector regression into a filtering process. Then we prove that the least squares support vector regression (LS-SVR) based on the translation invariant kernel is a linear time-invariant system. And we find that the common radial basis function kernel-based LS-SVR has properties of lowpass and linear phase filter in the applications to signal processing. By investigation, we find that different parameter selections have great effects on the frequency response of the LS-SVR filter. The simulation experiments for image denoising show that the radial basis function kernel-based LS-SVR filter works better than the adaptive Wiener filtering and wavelet transform-based method.