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.

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    $\begingroup$ Well, many of the more mathematical methods (I'm not sure I'd use "mathematical physics" here; functional analysis has come a long way since Hilbert) do not need any training data, for one thing, much less the massive amount that neural networks do. On the other hand, with enough training data, you can replicate the effect of any, e.g., variational method in a neural network, see arxiv.org/abs/1704.00447. In that sense, you're really comparing apples and oranges here -- either you have the data, or you don't. $\endgroup$ – Christian Clason Apr 27 '17 at 18:40

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