Parameter-free and fast nonlinear piecewise filtering. Application to experimental physics

TL;DR

This paper introduces a parameter-free, fast nonlinear filtering method for analyzing signals and images with piecewise homogeneous phases, especially effective in low signal-to-noise scenarios in experimental physics.

Contribution

It presents a unified nonlinear filtering approach with automated hyperparameter tuning, based on proximal algorithms and Stein estimator principles, suitable for large datasets.

Findings

Effective filtering of low SNR signals in physics experiments

Automated hyperparameter tuning enhances usability

Fast algorithms enable analysis of large datasets

Abstract

Numerous fields of nonlinear physics, very different in nature, produce signals and images, that share the common feature of being essentially constituted of piecewise homogeneous phases. Analyzing signals and images from corresponding experiments to construct relevant physical interpretations thus often requires detecting such phases and estimating accurately their characteristics (borders, feature differences, ...). However, situations of physical relevance often comes with low to very low signal to noise ratio precluding the standard use of classical linear filtering for analysis and denoising and thus calling for the design of advanced nonlinear signal/image filtering techniques. Additionally, when dealing with experimental physics signals/images, a second limitation is the large amount of data that need to be analyzed to yield accurate and relevant conclusions requiring the design of fast algorithms. The present work proposes a unified signal/image nonlinear filtering procedure, with fast algorithms and a data-driven automated hyperparameter tuning, based on proximal algorithms and Stein unbiased estimator principles. The interest and potential of these tools are illustrated at work on low-confinement solid friction signals and porous media multiphase flows.