Ridge-Aware Weighted Sparse Time-Frequency Representation

The ideal time-frequency (TF) representation which distributes the total energy along the instantaneous frequency (IF) of a signal is essentially sparse. Motivated by the weighted sparse representation of the signal, we propose the ridge-aware weighted sparse TF representation (RWSTF) which involves some properties an ideal TF representation should satisfy, such as, highly concentrated TF representation, the signal reconstruction and acceptable computational cost. Based on a basic sparse TF model, we firstly use a weighted strategy to effectively highlight the TF ridges even for the weak components, then fast iterative shrinkage thresholding algorithm (FISTA) is applied to obtain an efficient numerical approximation for solving the model. Furthermore, we introduce a k-sparsity strategy for the adaptive selection of the regularization parameter. A simulation study shows that the proposed method not only has higher energy concentration, but also performs better on signal denoising than other standard TF approaches, especially for the signals with fast varying IF. Two real life examples confirm the potential of the proposed method.