Finite Rate of Innovation Signal Reconstruction using Residual Neural Networks

The classical theory of sampling offers an accurate reconstruction of band-limited signals, however, not for the non band-limited. Over the previous decade, Finite Rate of Innovation (FRI) framework has emerged that has overcome this limitation. The FRI framework considers the sampling and reconstruction of particular classes of signals which are non-bandlimited and are fully specified by a finite number of degrees of freedom per unit interval. Traditional FRI algorithms, such as matrix pencil and Cadzow algorithm followed by annihilating filter methods use the singular value decomposition (SVD) for signal reconstruction. Eventhough, these algorithms achieve optimal results, however, in the low signal-to-noise ratio (SNR) they become unstable due to the larger magnitudes of the noise singular values than signal singular values. In this paper, to overcome this problem, a residual convolutional neural network approach, which estimates the signal parameters, is proposed. This network learns from the training data and gives the signal parameters from the discrete sample values. Simulation results show significant improvements on the smaller SNR values over the traditional FRI algorithms.