During the past few years several important areas of image processing and image classification or generation became dominated by convolutional neural networks.
I'm interested if there are any methods coming from mathematical physics context (like methods designed for solving ill-posed problems, spectral analysis, image deblurring and deringing), that outperform neural network-based approaches in 2017 for some common computer vision or image processing problem. Or methods that don't have any neural network-based rivals. Maybe in the field of biomedical image analysis (just a guess)?
The deeper and more specific the answer is, the better.