Spectrally adapted mercer kernels for support vector signal interpolation

Interpolation of nonuniformly sampled signals in the presence of noise is a hard and deeply analyzed problem. On the one hand, classical approaches like the Wiener filter use the second order statistics of the signal, and hence its spectrum, as a priori knowledge for finding the solution. On the other hand, Support Vector Machines (SVM) with Gaussian and sinc Mercer kernels have been previously proposed for time series interpolation, with good properties in terms of regularization and sparseness. Hence, in this paper we propose to use SVM-based algorithms with kernels having their spectra adapted to the signal spectrum, and to analyze their suitability for nonuniform interpolation. For this purpose, we investigate the performance of the SVM with autocorrelation kernels for one-dimensional time series interpolation. Simulations with synthetic signals show that SVM-based algorithms with the proposed kernels provide good performance for signals with different kinds of spectrum, even in the case of highly nonuniform sampling.