Self-supervised Bayesian Deep Learning for Image Recovery with Applications to Compressive Sensing

In recent years, deep learning emerges as one promising technique for solving many ill-posed inverse problems in image recovery, and most deep-learning-based solutions are based on supervised learning. Motivated by the practical value of reducing the cost and complexity of constructing labeled training datasets, this paper proposed a self-supervised deep learning approach for image recovery, which is dataset-free. Built upon Bayesian deep network, the proposed method trains a network with random weights that predicts the target image for recovery with uncertainty. Such uncertainty enables the prediction of the target image with small mean squared error by averaging multiple predictions. The proposed method is applied for image reconstruction in compressive sensing (CS), i.e., reconstructing an image from few measurements. The experiments showed that the proposed dataset-free deep learning method not only significantly outperforms traditional non-learning methods, but also is very competitive to the state-of-the-art supervised deep learning methods, especially when the measurements are few and noisy.