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.

A Two-step-training Deep Learning Framework for Real-time Computational Imaging without Physics Priors

Deep learning (DL) is a powerful tool in computational imaging for many applications. A common strategy is to reconstruct a preliminary image as the input of a neural network to achieve an optimized image. Usually, the preliminary image is acquired with the prior knowledge of the model. One outstanding challenge, however, is that the model is sometimes difficult to acquire with high accuracy. In this work, a two-step-training DL (TST-DL) framework is proposed for real-time computational imaging without prior knowledge of the model. A single fully-connected layer (FCL) is trained to directly learn the model with the raw measurement data as input and the image as output. Then, this pre-trained FCL is fixed and connected with an un-trained deep convolutional network for a second-step training to improve the output image fidelity. This approach has three main advantages. First, no prior knowledge of the model is required since the first-step training is to directly learn the model. Second, real-time imaging can be achieved since the raw measurement data is directly used as the input to the model. Third, it can handle any dimension of the network input and solve the input-output dimension mismatch issues which arise in convolutional neural networks. We demonstrate this framework in the applications of single-pixel imaging and photoacoustic imaging for linear model cases. The results are quantitatively compared with those from other DL frameworks and model-based optimization approaches. Noise robustness and the required size of the training dataset are studied for this framework. We further extend this concept to nonlinear models in the application of image de-autocorrelation by using multiple FCLs in the first-step training. Overall, this TST-DL framework is widely applicable to many computational imaging techniques for real-time image reconstruction without the physics priors.