On the exponential reproducing kernels for sampling signals with finite rate of innovation

Abstract

The theory of Finite Rate of Innovation (FRI) broadened the traditional sampling paradigm to certain classes of parametric signals. In the presence of noise, the original procedures are not as stable, and a different treatment is needed. In this paper we review the ideal FRI sampling scheme and some of the existing techniques to combat noise. We then present alternative denoising methods for the case of exponential reproducing kernels. We first vary existing subspace-based approaches. We also discuss how to design exponential reproducing kernels that are most robust to noise.