Time-frequency Scattering Transforms and Applications
Monday, January 29, 2018 - 3:15pm
Inspired by the success of deep learning, Mallat introduced the wavelet scattering transform and showed that it provides a useful representation of data. In contrast to his wavelet (time-scale) approach, we develop a Gabor (time-frequency) theory. To do this, we introduce the concept of a uniform covering frame, which is a generalization of traditional Gabor frames. When a uniform covering frame is incorporated into a scattering network, we obtain the Fourier scattering transform. This non-linear operator extracts time-frequency characteristics in a hierarchal manner by cascading convolutions with functions from a uniform covering frame and the complex modulus. It satisfies several provable properties that justify its use as a feature extractor for classification. We also extend this theory to rotationally invariant Fourier scattering transforms. Finally, we present some applications to anomaly detection in radiological data. This is joint work with Wojciech Czaja.