Signal recognition and adapted filtering by non-commutative tomography

Tomogram, a generalisation of the Radon transform to arbitrary pairs of non-commuting operators, is a positive bilinear transforms with a rigorous probabilistic interpretation which provides a full characterisation of the signal and is 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 the authors show that, even for noisy signals, meaningful time-resolved information may be obtained by the construction of an operator pair adapted to the signal.