Physics informed image restoration under low illumination with simultaneous parameter estimation using 3D integral imaging and Bayesian neural networks

Image restoration aims to recover a clean image given a noisy image. It has long been a topic of interest for researchers in imaging, optical science and computer vision. As the imaging environment becomes more and more deteriorated, the problem becomes more challenging. Several computational approaches, ranging from statistical to deep learning, have been proposed over the years to tackle this problem. The deep learning-based approaches provided promising image restoration results, but it's purely data driven and the requirement of large datasets (paired or unpaired) for training might demean its utility for certain physical problems. Recently, physics informed image restoration techniques have gained importance due to their ability to enhance performance, infer some sense of the degradation process and its potential to quantify the uncertainty in the prediction results. In this paper, we propose a physics informed deep learning approach with simultaneous parameter estimation using 3D integral imaging and Bayesian neural network (BNN). An image-image mapping architecture is first pretrained to generate a clean image from the degraded image, which is then utilized for simultaneous training with Bayesian neural network for simultaneous parameter estimation. For the network training, simulated data using the physical model has been utilized instead of actual degraded data. The proposed approach has been tested experimentally under degradations such as low illumination and partial occlusion. The recovery results are promising despite training from a simulated dataset. We have tested the performance of the approach under varying levels of illumination condition. Additionally, the proposed approach also has been analyzed against corresponding 2D imaging-based approach. The results suggest significant improvements compared to 2D even training under similar datasets. Also, the parameter estimation results demonstrate the utility of the approach in estimating the degradation parameter in addition to image restoration under the experimental conditions considered.