The role of nonlinear activations in Fourier-domain neural networks: Noise resilience, regularization, blurring and autocorrelation artifact

Motivation: Extending explainable Artificial Intelligence to Fourier-domain deep neural networks. Goal(s): To illuminate the impact of nonlinear activations in Fourier-domain neural networks for interpolation on noise resilience in image space. Approach: An image space formalism for convolutional neural networks for Fourier-domain interpolation is used to inspect the activation part, which is linked to noise resilience in image space, in a human-readable manner. The nonlinearity-degree in the model is controlled via the negative slope parameter of leaky ReLU activation. Results: The negative slope in non-linear ReLU activation may serve as regularization parameter, allowing to adjust tradeoff between image blurring, autocorrelation artifact and noise resilience. Impact: This work illuminates the role of nonlinearity in robust artificial neural networks for Fourier-domain interpolation via activated convolution layers at limited training data and shows possible implications of noise resilience, image blurring and autocorrelation artifacts in the image center.