Atomic Norm Soft Thresholding for Sparse Time-frequency Representation

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.