Convolve and Conquer: Data Comparison with Wiener Filter

Quantitative evaluations of differences and/or similarities between data samples define and shape optimisation problems associated with learning data distributions. Current methods to compare data often suffer from limitations in capturing such distributions or lack desirable mathematical properties for optimisation (e.g. smoothness, differentiability, or convexity). In this paper, we introduce a new method to measure (dis)similarities between paired samples inspired by Wiener-filter theory. The convolutional nature of Wiener filters allows us to comprehensively compare data samples in a globally correlated way. We validate our approach in two machine learning applications focused on medical imaging problems: Magnetic Resonance Imaging (MRI) data imputation and non-parametric generative modelling. Our results demonstrate increased resolution in reconstructed images with better perceptual quality and higher data fidelity compared to analogue conventional mean-squared-error implementations.