Interpretable Super-Resolution via a Learned Time-Series Representation

Randall Balestriero, Hervé Glotin, Richard Baraniuk

Keywords: time frequency representation, time series, wigner ville, cohen class, wavelet transform, scalogram, bird, speech

Abstract:

We develop an interpretable and learnable Wigner-Ville distribution that produces a super-resolved quadratic signal representation for time-series analysis.
Our approach has two main hallmarks.
First, it interpolates between known time-frequency representations (TFRs) in that it can reach super-resolution with increased time and frequency resolution beyond what the Heisenberg uncertainty principle prescribes and thus beyond commonly employed TFRs,
Second, it is interpretable thanks to an explicit low-dimensional and physical parametrization of the Wigner-Ville distribution.
We demonstrate that our approach is able to learn highly adapted TFRs and is ready and able to tackle various large-scale classification tasks, where we reach state-of-the-art performance compared to baseline and learned TFRs.

One-sentence Summary: We develop an interpretable and learnable Wigner-Ville distribution that produces a super-resolved quadratic signal representation for time-series analysis.

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