  Neuromorphic sampling is a bioinspired and opportunistic analog-to-digital
conversion technique, where the measurements are recorded only when there is a
significant change in the signal amplitude. Neuromorphic sampling has paved the
way for a new class of vision sensors called event cameras or dynamic vision
sensors (DVS), which consume low power, accommodate a high-dynamic range, and
provide sparse measurements with high temporal resolution making it convenient
for downstream inference tasks. In this paper, we consider neuromorphic sensing
of signals with a finite rate of innovation (FRI), including a stream of Dirac
impulses, sum of weighted and time-shifted pulses, and piecewise-polynomial
functions. We consider a sampling-theoretic approach and leverage the close
connection between neuromorphic sensing and time-based sampling, where the
measurements are encoded temporally. Using Fourier-domain analysis, we show
that perfect signal reconstruction is possible via parameter estimation using
high-resolution spectral estimation methods. We develop a kernel-based sampling
approach, which allows for perfect reconstruction with a sample complexity
equal to the rate of innovation of the signal. We provide sufficient conditions
on the parameters of the neuromorphic encoder for perfect reconstruction.
Furthermore, we extend the analysis to multichannel neuromorphic sampling of
FRI signals, in the single-input multi-output (SIMO) and multi-input
multi-output (MIMO) configurations. We show that the signal parameters can be
jointly estimated using multichannel measurements. Experimental results are
provided to substantiate the theoretical claims.
