Sparse-Prony FRI signal reconstruction

Abstract

Finite rate of innovation (FRI) approach is used for sampling and reconstruction of a class of non-bandlimited continuous signals having a finite number of free parameters. Traditionally, Prony and matrix-pencil methods are proposed to reconstruct FRI signals from the discrete samples. However, these methods tend to break down at a certain signal-to-noise ratio (SNR). In this paper, we propose sparsity-based annihilating filter, refer it as sparse-Prony, which avoids polynomial root-finding. In the noiseless scenario, the proposed method is able to recover perfectly the original signal. Simulation results for the noisy scenario demonstrate significant improvement in the performance in terms of MSE over the traditional FRI methods, especially in the breakdown SNR. © 2023, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.