  Neuromorphic sampling is a paradigm shift in analog-to-digital conversion
where the acquisition strategy is opportunistic and measurements are recorded
only when there is a significant change in the signal. Neuromorphic sampling
has given rise to a new class of event-based sensors called dynamic vision
sensors or neuromorphic cameras. The neuromorphic sampling mechanism utilizes
low power and provides high-dynamic range sensing with low latency and high
temporal resolution. The measurements are sparse and have low redundancy making
it convenient for downstream tasks. In this paper, we present a
sampling-theoretic perspective to neuromorphic sensing of continuous-time
signals. We establish a close connection between neuromorphic sampling and
time-based sampling - where signals are encoded temporally. We analyse
neuromorphic sampling of signals in shift-invariant spaces, in particular,
bandlimited signals and polynomial splines. We present an iterative technique
for perfect reconstruction subject to the events satisfying a density
criterion. We also provide necessary and sufficient conditions for perfect
reconstruction. Owing to practical limitations in meeting the sufficient
conditions for perfect reconstruction, we extend the analysis to approximate
reconstruction from sparse events. In the latter setting, we pose signal
reconstruction as a continuous-domain linear inverse problem whose solution can
be obtained by solving an equivalent finite-dimensional convex optimization
program using a variable-splitting approach. We demonstrate the performance of
the proposed algorithm and validate our claims via experiments on synthetic
signals.
