Atomic Norm Soft Thresholding for Sparse Time-frequency Representation

TL;DR

This paper introduces a novel atomic norm soft thresholding method for sparse time-frequency representation, improving localization accuracy of non-stationary signals by leveraging atomic norm-based sparse optimization.

Contribution

The paper proposes a new atomic norm soft thresholding technique for enhanced sparse time-frequency analysis, ensuring accurate localization under strong duality.

Findings

Performance surpasses conventional methods in numerical experiments

Ensures accurate TF localization

Leverages atomic norm for sparse optimization

Abstract

Time-frequency (TF) representation of non-stationary signals typically requires the effective concentration of energy distribution along the instantaneous frequency (IF) ridge, which exhibits intrinsic sparsity. Inspired by the sparse optimization over continuum via atomic norm, a novel atomic norm soft thresholding for sparse TF representation (AST-STF) method is proposed, which ensures accurate TF localization under the strong duality. Numerical experiments demonstrate that the performance of the proposed method surpasses that of conventional methods.