Convolve and Conquer: Data Comparison with Wiener Filters

TL;DR

This paper introduces a novel data comparison method based on Wiener filters, enabling more comprehensive and mathematically desirable evaluations of data similarities across various machine learning tasks.

Contribution

It presents a new Wiener filter-inspired approach for data comparison that improves upon existing methods in capturing distributions and optimizing data analysis.

Findings

Enhanced image reconstruction resolution and perceptual quality

Improved robustness against translations in data comparison

Better data fidelity in multiple applications

Abstract

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 four machine learning applications: data compression, medical imaging imputation, translated classification, and non-parametric generative modelling. Our results demonstrate increased resolution in reconstructed images with better perceptual quality and higher data fidelity, as well as robustness against translations, compared to conventional mean-squared-error analogue implementations.