来自光子的比特：使用二进制泊松统计的过采样图像采集
Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics
摘要：
我们研究了一种新的图像传感器，它让人想起传统的摄影胶片。传感器中的每个像素都有一个二进制响应，仅给出局部光强度的一位量化测量。为了分析其性能，我们制定的过采样二进制传感方案的参数估计问题的基础上量化泊松统计。我们表明，与单光子量化阈值和大的过采样因子，Cramér-Rao下界（CRLB）的估计方差接近一个理想的未量化的传感器，也就是说，如果没有量化的传感器测量。此外，CRLB被证明是渐近实现的最大似然估计（MLE）。通过证明我们的问题的对数似然函数是凹的，我们保证了迭代算法的全局最优性。对合成数据和原型传感器拍摄的图像的数值结果验证了我们的理论分析，并证明了我们的图像重建算法的有效性。他们还建议过采样二进制传感方案在高动态范围摄影的潜在应用。
英文摘要：
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 Cramér-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.
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