Non-commutative tomography: A tool for data analysis and signal processing

TL;DR

This paper introduces non-commutative tomograms as a robust data analysis and signal processing tool, providing explicit constructions for various operator pairs and demonstrating applications in denoising and signal detection.

Contribution

It presents a novel framework for non-commutative tomograms, extending the Radon transform to non-commuting operators with practical applications.

Findings

Effective noise robustness demonstrated

Successful detection of small signals

Component separation capabilities shown

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. We provide an explicit construction of tomogram transforms for many pairs of noncommuting operators in one and two dimensions and illustrations of their use for denoising, detection of small signals and component separation.