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The Neural Tangent Link Between CNN Denoisers and Non-Local Filters

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Document pages: 25 pages

Abstract: Convolutional Neural Networks (CNNs) are now a well-established tool forsolving computational imaging problems. Modern CNN-based algorithms obtainstate-of-the-art performance in diverse image restoration problems.Furthermore, it has been recently shown that, despite being highlyoverparameterized, networks trained with a single corrupted image can stillperform as well as fully trained networks. We introduce a formal link betweensuch networks through their neural tangent kernel (NTK), and well-knownnon-local filtering techniques, such as non-local means or BM3D. The filteringfunction associated with a given network architecture can be obtained in closedform without need to train the network, being fully characterized by the randominitialization of the network weights. While the NTK theory accurately predictsthe filter associated with networks trained using standard gradient descent,our analysis shows that it falls short to explain the behaviour of networkstrained using the popular Adam optimizer. The latter achieves a larger changeof weights in hidden layers, adapting the non-local filtering function duringtraining. We evaluate our findings via extensive image denoising experiments.

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