Reconstruction of FRI Signals using Autoencoders with Fixed Decoders

Finite Rate of Innovation (FRI) theory considers sampling and reconstruction of classes of non-bandlimited signals that have a small number of free parameters. The task of reconstructing continuous FRI signals from discrete samples is often transformed into a spectral estimation problem and solved using methods involving estimating signal subspaces. These techniques tend to break down at a certain peak signal-to-noise ratio (PSNR). To avoid this inherent breakdown, we consider an alternative learning-based approach that uses autoencoders with fixed decoders. We propose to determine the parameters of the decoders based on the information of the sampling kernel explicitly. The fixed decoders provide a regularizing effect on the output of the encoder and lead to a robust network. Simulations show significant improvements on the breakdown PSNR over both classical subspace-based methods and our previous work based on deep neural networks.