  Light detection and ranging systems reconstruct scene depth from
time-of-flight measurements. For low light-level depth imaging applications,
such as remote sensing and robot vision, these systems use single-photon
detectors that resolve individual photon arrivals. Even so, they must detect a
large number of photons to mitigate Poisson shot noise and reject anomalous
photon detections from background light. We introduce a novel framework for
accurate depth imaging using a small number of detected photons in the presence
of an unknown amount of background light that may vary spatially. It employs a
Poisson observation model for the photon detections plus a union-of-subspaces
constraint on the discrete-time flux from the scene at any single pixel.
Together, they enable a greedy signal-pursuit algorithm to rapidly and
simultaneously converge on accurate estimates of scene depth and background
flux, without any assumptions on spatial correlations of the depth or
background flux. Using experimental single-photon data, we demonstrate that our
proposed framework recovers depth features with 1.7 cm absolute error, using 15
photons per image pixel and an illumination pulse with 6.7-cm scaled
root-mean-square length. We also show that our framework outperforms the
conventional pixelwise log-matched filtering, which is a
computationally-efficient approximation to the maximum-likelihood solution, by
a factor of 6.1 in absolute depth error.
