Root-Free Annihilating Filter Method for Sparse Signal Reconstruction

Abstract

Traditionally, annihilating filter approach (a.k.a Prony’s approach), universal finite rate of innovation (FRI), and compressed sensing algorithms have been presented to solve the sparse reconstruction problem when the measurement matrix has Fourier bases. However, annihilating filter approach requires computing the polynomial roots of the annihilating filter, and this fact yields an unstable recovery of sparse signal in the high noise environment. In this paper, we present a polynomial root-free annihilating filter approach for reconstructing sparse signals based on the padding of missing measurement values to acquired measurements. The method accomplishes complete reconstruction accuracy of sparse signals in the noiseless environment. Moreover, the superior reconstruction accuracy of the proposed root-free annihilating filter approach, in comparison with the traditional annihilating filter approach and universal FRI, is proved by experimental simulations in the existence of a low signal-to-noise ratio. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.