This paper addresses the challenging issue of recovery by interpolation of nonuniformly sampled signals, corrupted by additive, zero-mean noise. The reconstruction of a continuous signal from its nonuniformly distributed samples is inherently met in many domains, including medicine and data communication. The authors present a “continuous-time equivalent system for nonuniform interpolation (CESNI),” a solution based on the support vector machine (SVM) approach.
Inspired by frequency domain interpretations of the originating Yen’s algorithm and of the Wiener filters, the authors choose to explore a number of spectrally adapted kernels. They investigate several Mercer kernels, modulated versions of radial basis function (RBF) and sinc kernels, or autocorrelation based. A number of experiments explore the algorithms’ behavior in the case of bandpass signals, their spectral adaptation abilities, performance issues of SVM kernels, and their rapport to the Yen and Wiener approaches. Some of the experiments are carried out on synthetic signals, degraded with different types of non-Gaussian noise, with various levels of nonuniformity, and samples rate. The closing part of the experiment section presents an interesting real-life application: the analysis and reconstruction of the heart rate variability (HRV) signal, operated to investigate heart conditions. The evaluation concerns the algorithms’ robustness against non-Gaussian noise and is made in terms of ratio between the spectrum of the signal and that of the error. The experimental results show that the SVM methodology modeled on autocorrelation kernels behaves the best.
The paper is remarkable by its interesting content, the minute and proper exposition of the theoretical and experimental issues. It is supplemented with a very extensive and useful bibliography. It would be worth reading for signal processing specialists.