Deep-learning-driven Reliable Single-pixel Imaging with Uncertainty Approximation

Single-pixel imaging (SPI) has the advantages of high-speed acquisition over a broad wavelength range and system compactness, which are difficult to achieve by conventional imaging sensors. However, a common challenge is low image quality arising from undersampling. Deep learning (DL) is an emerging and powerful tool in computational imaging for many applications and researchers have applied DL in SPI to achieve higher image quality than conventional reconstruction approaches. One outstanding challenge, however, is that the accuracy of DL predictions in SPI cannot be assessed in practical applications where the ground truths are unknown. Here, we propose the use of the Bayesian convolutional neural network (BCNN) to approximate the uncertainty (coming from finite training data and network model) of the DL predictions in SPI. Each pixel in the predicted result from BCNN represents the parameter of a probability distribution rather than the image intensity value. Then, the uncertainty can be approximated with BCNN by minimizing a negative log-likelihood loss function in the training stage and Monte Carlo dropout in the prediction stage. The results show that the BCNN can reliably approximate the uncertainty of the DL predictions in SPI with varying compression ratios and noise levels. The predicted uncertainty from BCNN in SPI reveals that most of the reconstruction errors in deep-learning-based SPI come from the edges of the image features. The results show that the proposed BCNN can provide a reliable tool to approximate the uncertainty of DL predictions in SPI and can be widely used in many applications of SPI.