Spectrally adapted Mercer kernels for support vector nonuniform interpolation

Interpolation of nonuniformly sampled signals in the presence of noise is a widely analyzed problem in signal processing applications. Interpolators based on Support Vector Machines (SVM) with Gaussian and sinc Mercer kernels have been previously proposed, obtaining good performance in terms of regularization and sparseness. In this paper, inspired in the classical spectral interpretation of the Wiener filter, we explore the impact of adapting the spectrum of the SVM kernel to that of the observed signal. We provide a theoretical foundation for this approach based on a continuous-time equivalent system for interpolation. We study several kernels with different degrees of spectral adaptation to band-pass signals, namely, modulated kernels and autocorrelation kernels. The proposed algorithms are evaluated with extensive simulations with synthetic signals and an application example with real data. Our approach is compared with SVM with Gaussian and sinc kernels and with other well known interpolators. The SVM with autocorrelation kernel provides the highest performance in terms of signal to error ratio in several scenarios. We conclude that the estimated (or actual if known) autocorrelation of the observed sequence can be straightforwardly used as a spectrally adapted kernel, outperforming the classic SVM with low pass kernels for nonuniform interpolation.