On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data

TL;DR

This paper investigates the conditions under which sparse time-frequency decompositions of multiscale data are unique and demonstrates that nonlinear matching pursuit can effectively approximate this unique decomposition.

Contribution

It provides a theoretical analysis of the uniqueness of sparse time-frequency representations and evaluates the efficiency of nonlinear matching pursuit for multiscale data.

Findings

Sparse time frequency decomposition is unique under scale separation.

Nonlinear matching pursuit can approximate the unique decomposition effectively.

The error in the decomposition is bounded by the scale separation property.

Abstract

In this paper, we analyze the uniqueness of the sparse time frequency decomposition and investigate the efficiency of the nonlinear matching pursuit method. Under the assumption of scale separation, we show that the sparse time frequency decomposition is unique up to an error that is determined by the scale separation property of the signal. We further show that the unique decomposition can be obtained approximately by the sparse time frequency decomposition using nonlinear matching pursuit.