Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics

TL;DR

This paper introduces a binary photon-based image sensor with oversampling that, under certain conditions, achieves estimation performance close to ideal sensors, enabling high dynamic range imaging with simple binary measurements.

Contribution

It formulates oversampled binary photon sensing as a parameter estimation problem, demonstrating near-optimal performance and practical algorithms for image reconstruction.

Findings

CRLB approaches that of unquantized sensors with oversampling

MLE achieves asymptotic optimality in estimation

Numerical results confirm theoretical analysis and high dynamic range potential

Abstract

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.