  We study a new image sensor that is reminiscent of traditional photographic
film. Each pixel in the sensor has a binary response, giving only a one-bit
quantized measurement of the local light intensity. To analyze its performance,
we formulate the oversampled binary sensing scheme as a parameter estimation
problem based on quantized Poisson statistics. We show that, with a
single-photon quantization threshold and large oversampling factors, the
Cram\'er-Rao lower bound (CRLB) of the estimation variance approaches that of
an ideal unquantized sensor, that is, as if there were no quantization in the
sensor measurements. Furthermore, the CRLB is shown to be asymptotically
achievable by the maximum likelihood estimator (MLE). By showing that the
log-likelihood function of our problem is concave, we guarantee the global
optimality of iterative algorithms in finding the MLE. Numerical results on
both synthetic data and images taken by a prototype sensor verify our
theoretical analysis and demonstrate the effectiveness of our image
reconstruction algorithm. They also suggest the potential application of the
oversampled binary sensing scheme in high dynamic range photography.
