Sparse time-frequency representation via atomic norm minimization

TL;DR

This paper introduces a novel atomic norm-based method for sparse time-frequency representation of nonstationary signals, avoiding discretization issues and achieving sparser, better-localized T-F representations.

Contribution

The paper proposes a continuous-parameter sparse T-F representation method using atomic norm minimization, eliminating grid mismatch problems of prior $ ext{l}_1$-norm approaches.

Findings

T-F representations are sparser than conventional methods.

The proposed method improves localization of nonstationary signals.

Numerical experiments validate the effectiveness of the atomic norm approach.

Abstract

Nonstationary signals are commonly analyzed and processed in the time-frequency (T-F) domain that is obtained by the discrete Gabor transform (DGT). The T-F representation obtained by DGT is spread due to windowing, which may degrade the performance of T-F domain analysis and processing. To obtain a well-localized T-F representation, sparsity-aware methods using $\ell_1$-norm have been studied. However, they need to discretize a continuous parameter onto a grid, which causes a model mismatch. In this paper, we propose a method of estimating a sparse T-F representation using atomic norm. The atomic norm enables sparse optimization without discretization of continuous parameters. Numerical experiments show that the T-F representation obtained by the proposed method is sparser than the conventional methods.