HDR Imaging with Quanta Image Sensors: Theoretical Limits and Optimal Reconstruction

High dynamic range (HDR) imaging is one of the biggest achievements in modern photography. Traditional solutions to HDR imaging are designed for and applied to CMOS image sensors (CIS). However, the mainstream one-micron CIS cameras today generally have a high read noise and low frame-rate. These, in turn, limit the acquisition speed and quality, making the cameras slow in the HDR mode. In this paper, we propose a new computational photography technique for HDR imaging. Recognizing the limitations of CIS, we use the Quanta Image Sensor (QIS) to trade the spatial-temporal resolution with bit-depth. QIS is a single-photon image sensor that has comparable pixel pitch to CIS but substantially lower dark current and read noise. We provide a complete theoretical characterization of the sensor in the context of HDR imaging, by proving the fundamental limits in the dynamic range that QIS can offer and the trade-offs with noise and speed. In addition, we derive an optimal reconstruction algorithm for single-bit and multi-bit QIS. Our algorithm is theoretically optimal for \emph{all} linear reconstruction schemes based on exposure bracketing. Experimental results confirm the validity of the theory and algorithm, based on synthetic and real QIS data.