Fast compressive measurements acquisition using optimized binary sensing matrices for low-light-level imaging

Compressive measurements benefit low-light-level imaging (L³-imaging) due to the significantly improved measurement signal-to-noise ratio (SNR). However, as with other compressive imaging (CI) systems, compressive L³-imaging is slow. To accelerate the data acquisition, we develop an algorithm to compute the optimal binary sensing matrix that can minimize the image reconstruction error. First, we make use of the measurement SNR and the reconstruction mean square error (MSE) to define the optimal gray-value sensing matrix. Then, we construct an equality-constrained optimization problem to solve for a binary sensing matrix. From several experimental results, we show that the latter delivers a similar reconstruction performance as the former, while having a smaller dynamic range requirement to system sensors.