Oversampled Noisy Binary Image Sensor

We study the oversampled binary image sensor in [1] under noisy scenario. The binary image sensor is similar to traditional photographic film with pixel value equal to "0" or "1". The potential application of the oversampled binary image sensor is high dynamic range imaging. Since the pixel value is binary, we model the noise as additive Bernoulli noise. We focus on the case that the threshold in the binary sensor is equal to a single photon. Because of noise, the dynamic range of the sensor is reduced. But the image sensor is quite robust to noise when the light intensity value is large. We use maximum-likelihood estimator (MLE) to reconstruct the light intensity field, and prove that when the threshold is a single photon, even if there is noise, the log-likelihood function is still concave, which guarantees to find the global optimal solution. Experimental results for 1-D signal and 2-D images verify our performance analysis and show the effectiveness of the reconstruction algorithm.