  The one-bit quanta image sensor (QIS) is a photon-counting device that
captures image intensities using binary bits. Assuming that the analog voltage
generated at the floating diffusion of the photodiode follows a
Poisson-Gaussian distribution, the sensor produces either a ``1'' if the
voltage is above a certain threshold or ``0'' if it is below the threshold. The
concept of this binary sensor has been proposed for more than a decade, and
physical devices have been built to realize the concept. However, what benefits
does a one-bit QIS offer compared to a conventional multi-bit CMOS image
sensor? Besides the known empirical results, are there theoretical proofs to
support these findings?
  The goal of this paper is to provide new theoretical support from a signal
processing perspective. In particular, it is theoretically found that the
sensor can offer three benefits: (1) Low-light: One-bit QIS performs better at
low-light because it has a low read noise, and its one-bit quantization can
produce an error-free measurement. However, this requires the exposure time to
be appropriately configured. (2) Frame rate: One-bit sensors can operate at a
much higher speed because a response is generated as soon as a photon is
detected. However, in the presence of read noise, there exists an optimal frame
rate beyond which the performance will degrade. A Closed-form expression of the
optimal frame rate is derived. (3) Dynamic range: One-bit QIS offers a higher
dynamic range. The benefit is brought by two complementary characteristics of
the sensor: nonlinearity and exposure bracketing. The decoupling of the two
factors is theoretically proved, and closed-form expressions are derived.
