  Quanta Image Sensor (QIS) is a binary imaging device envisioned to be the
next generation image sensor after CCD and CMOS. Equipped with a massive number
of single photon detectors, the sensor has a threshold $q$ above which the
number of arriving photons will trigger a binary response "1", or "0"
otherwise. Existing methods in the device literature typically assume that
$q=1$ uniformly. We argue that a spatially varying threshold can significantly
improve the signal-to-noise ratio of the reconstructed image. In this paper, we
present an optimal threshold design framework. We make two contributions.
First, we derive a set of oracle results to theoretically inform the maximally
achievable performance. We show that the oracle threshold should match exactly
with the underlying pixel intensity. Second, we show that around the oracle
threshold there exists a set of thresholds that give asymptotically unbiased
reconstructions. The asymptotic unbiasedness has a phase transition behavior
which allows us to develop a practical threshold update scheme using a
bisection method. Experimentally, the new threshold design method achieves
better rate of convergence than existing methods.
