A finite rate of innovation approach for the estimation of a stream of decaying exponentials.

In this paper we describe a novel approach for sparse signal estimation from low-pass filtered observations. Motivated by applications in neuroscience, we consider the problem of retrieving the time instants of a train of pulses where the shape of the pulse is a causal decaying exponential. Our approach builds upon recent results on continuous sparse signal recovery using the finite rate of innovation framework. Our results show that our method achieves near to optimal performance in terms of signal recovery on synthetically generated data. We then explore its potential application to neural activity inference from calcium imaging fluorescence traces, and propose an algorithm based on the proposed estimation method that is applicable to real calcium fluorescence signals of arbitrary length.