A Generalized Approach for Recovering Time Encoded Signals with Finite Rate of Innovation

Abstract: In this paper, we consider the problem of recovering a sum of filtered Diracs, representing an input with finite rate of innovation (FRI), from its corresponding time encoding machine (TEM) measurements. So far, the recovery was guaranteed for cases where the filter is selected from a number of particular mathematical functions. Here, we introduce a new generalized method for recovering FRI signals from the TEM output. On the theoretical front, we significantly increase the class of filters for which reconstruction is guaranteed, and provide a condition for perfect input recovery depending on the first two local derivatives of the filter. We extend this result with reconstruction guarantees in the case of noise corrupted FRI signals. On the practical front, in cases where the filter has an unknown mathematical function, the proposed method streamlines the recovery process by bypassing the filter modelling stage. We validate the proposed method via numerical simulations with filters previously used in the literature, as well as filters that are not compatible with the existing results. Additionally, we validate the results using a TEM hardware implementation.