Universal Discrete Finite Rate of Innovation Scheme for Sparse Signal Reconstruction

Finite rate of innovation (FRI) schemes have been proposed to reconstruct a class of discrete-time signals having small number of nonzero coefficients (sparse signals) from a limited number of observations. However, these reconstruction schemes achieve optimal performance up to a certain signal-to-noise ratio (SNR) and breakdown for smaller SNR values. Moreover, these are not universal as they are aware of the number of nonzero coefficients (a.k.a. L0 norm) for reconstruction of the signal. In this paper, we propose a novel FRI reconstruction scheme based on error decrease detector criterion to extend the current scheme to a universal one which enables reconstructing signals with an unknown number of nonzero coefficients. With noiseless conditions, we show that the proposed FRI scheme achieves perfect reconstruction of the original signal. And also, computer simulations for the noisy case are presented where the proposed scheme shows improvements over the traditional FRI scheme in the breakdown SNR. Further, an application of the proposed universal FRI scheme on reconstruction of magnetic resonance images and QRS complexes is demonstrated.