Signal recognition and adapted filtering by non-commutative tomography

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.

arXiv comment19 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1107.0929