  Active 3D imaging systems have broad applications across disciplines,
including biological imaging, remote sensing and robotics. Applications in
these domains require fast acquisition times, high timing resolution, and high
detection sensitivity. Single-photon avalanche diodes (SPADs) have emerged as
one of the most promising detector technologies to achieve all of these
requirements. However, these detectors are plagued by measurement distortions
known as pileup, which fundamentally limit their precision. In this work, we
develop a probabilistic image formation model that accurately models pileup. We
devise inverse methods to efficiently and robustly estimate scene depth and
reflectance from recorded photon counts using the proposed model along with
statistical priors. With this algorithm, we not only demonstrate improvements
to timing accuracy by more than an order of magnitude compared to the
state-of-the-art, but this approach is also the first to facilitate
sub-picosecond-accurate, photon-efficient 3D imaging in practical scenarios
where widely-varying photon counts are observed.
