Time Encoding of Sparse Signals with Flexible Filters

In this work, we consider the problem of recovering a sparse signal consisting of a sum of filtered spikes from the output of a time encoding machine (TEM). This problem was addressed before with recovery methods designed for filters with specific shapes, mostly relying on Prony’s method for recovery. Here we propose a new recovery method for sparse inputs from TEM samples. Compared to existing approaches, the new method relaxes significantly the assumption on the filters. The method is associated by a theoretically guaranteed algorithm. We provide numerical examples to evaluate the new method, including an example with filters that are not compatible with previous methods.