Signal recognition and adapted filtering by non-commutative tomography

TL;DR

This paper introduces a novel non-commutative tomogram approach for signal recognition and filtering, enabling effective extraction of meaningful information with high time resolution even in noisy environments.

Contribution

It presents an adaptive operator pair construction for tomograms, improving signal analysis and noise robustness over traditional methods.

Findings

Enhanced signal component separation in noisy conditions

Improved time resolution in signal analysis

Robustness of the method against noise

Abstract

Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are robust in the presence of noise. Tomograms based on the time-frequency operator pair, were used in the past for component separation and denoising. Here we show how, by the construction of an operator pair adapted to the signal, meaningful information with good time resolution is extracted even in very noisy situations.