Rotationally invariant time-frequency scattering transforms

TL;DR

This paper introduces rotationally invariant time-frequency scattering transforms using directional functions called uniform covering frames, with proven invariance, stability, and boundedness properties.

Contribution

It develops a new class of rotationally invariant scattering transforms based on uniform covering frames, extending time-frequency analysis with directional sensitivity.

Findings

Proves invariance and stability of the proposed transforms.

Constructs finite uniform covering frames.

Establishes boundedness and non-expansiveness.

Abstract

In this paper we construct directionally sensitive functions that can be viewed as directional time-frequency representations. We call such a sequence a rotational uniform covering frame and by studying rotations of the frame, we derive the rotational Fourier scattering transform and the truncated rotational Fourier scattering transform. We prove that both operators are rotationally invariant, are bounded above and below, are non-expansive, and contract small translations and additive diffeomorphisms. We also construct finite uniform covering frames.