Signal recognition and adapted filtering by non-commutative tomography

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.

💡 Research Summary

The paper introduces a novel signal‑analysis framework called non‑commutative tomography, which extends the classical Radon transform to arbitrary pairs of non‑commuting operators. A tomogram is defined as the set of probability distributions obtained by projecting a signal onto the eigenfunctions of the operator family
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