(untitled) (CSIAM Transactions on Applied Mathematics, 2020)
Image inverse problem aims to reconstruct or restore high-quality images from observed samples or degraded images, with wide applications in imaging sciences. The traditional methods rely on mathematical models to invert the process of image sensing or degradation. But these methods require good design of image prior or regularizer that is hard to be hand-crafted. In recent years, deep learning has been introduced to image inverse problems by learning to invert image sensing or degradation process. In this paper, we will review a new trend of methods for image inverse problem that combines the imaging/degradation model with deep learning approach. These methods are typically designed by unrolling some optimization algorithms or statistical inference algorithms into deep neural networks. The ideas combining deep learning and models are also emerging in other fields such as PDE, control, etc. We will also summarize and present perspectives along this research direction.