Image denoising—Old and new

Image Denoising is among the most fundamental problems in image processing, not only for the sake of improving the image quality, but also as the first proof-of-concept for the development of virtually any new regularization term for inverse problems in imaging. While variational methods have represented the state of the art for several decades, they are recently being challenged by (deep) learning-based approaches. In this chapter, we review some of the most successful variational approaches for image reconstruction and discuss their structural advantages and disadvantages in comparison to learning-based approaches. Furthermore, we present a framework to incorporate deep learning approaches in inverse problem formulations, so as to leverage the descriptive power of deep learning with the flexibility of inverse problems’ solvers. Different algorithmic schemes are derived from replacing the regularizing subproblem of common optimization algorithms by neural networks trained on image denoising. We conclude from several experiments that such techniques are very promising but further studies are needed to understand to what extent and in which settings the power of the data-driven network transfers to a better overall performance.