Noncommutative tomography: A tool for data analysis and signal processing

Tomograms, a generalization of the Radon transform to arbitrary pairs of noncommuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation that 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 a robust characterization of many different signals. Here we provide an explicit construction of tomogram transforms for many other pairs of noncommuting operators in one and two dimensions and describe how they are used for denoising, component separation, and filtering.