Sequential local FRI sampling of infinite streams of Diracs

The theory of sampling signals with finite rate of innovation (FRI) has shown that it is possible to perfectly recover classes of non-bandlimited signals such as streams of Diracs from uniform samples. Most of previous papers, however, have to some extent only focused on the sampling of periodic or finite duration signals. In this paper we propose a novel method that is able to reconstruct infinite streams of Diracs, even in high noise scenarios. We sequentially process the discrete samples and output locations and amplitudes of the Diracs in real-time. We first establish conditions for perfect reconstruction in the noiseless case and then present the sequential algorithm for the noisy scenario. We also show that we can achieve a high reconstruction accuracy of 1000 Diracs for SNRs as low as 5dB.