Sparse Gabor Time-Frequency Representation Based on ℓ_(1/2)-ℓ_2 Regularization

摘要

The discrete Gabor transform (DGT) is an important and widely used time-frequency analysis tool in signal processing. In this paper, a sparse time-frequency representation (TFR) method based on the DGT is studied using mixed l(1/2)-l(2) norm regularization which can overcome the over-sparse problem and permit a better sparsity and stability. Because the width of the window function in the DGT directly affects the time-frequency resolution and concentration of the Gabor spectrum, an adaptive optimal window width (AOWW) selection algorithm based on information entropy theory can be applied to search for the optimal width in the DGT. In this paper, the traditional DGT is converted into a constraint optimization problem by minimizing a mixed l(1/2)-l(2) norm sparse constraint of the Gabor coefficients. The numerical experimental results show that the proposed sparsity-based TFR based on the conventional DGT is an effective and powerful tool for analyzing and processing nonstationary signals, obtaining a higher time-frequency concentration and sparsity of the Gabor TFR of a given signal.