Deep learning approaches to inverse problems in imaging: Past, present and future

In recent years, deep learning-based models have gained momentum in imaging problems such as image and video super-resolution, image restoration or inpainting. The analytical approaches that have traditionally been used to solve image inverse problems have started to be replaced by deep learning ones, being outperformed in terms of efficacy and efficiency in many applications. However, deep learning-based models lack the adaptability of analytical models, thus making them unsuitable for dealing simultaneously with different forward image formation models. In contrast to analytical methods, deep learning models typically do not use domain knowledge and rely on learning the solution to the inverse problem from large data sets. This is making them susceptible to errors caused by the presence of degradations not seen during training. Hybrid models combining analytical and deep learning approaches have been introduced to solve such generalization issues while retaining the efficacy of deep learning models. In this work, we review deep learning and hybrid methods for solving imaging inverse problems, focusing on image and video super-resolution and image restoration. Furthermore, we discuss open problems in this area that would be of critical importance in the future, the challenges of applying deep learning models to solve them, and how future research could address them.