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.

中文翻译：

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岭感知加权稀疏时频表示

沿着信号的瞬时频率（IF）分配总能量的理想时频（TF）表示基本上是稀疏的。出于信号的稀疏表示的动机，我们提出了具有脊意识的加权稀疏TF表示（RWSTF），它涉及理想TF表示应满足的一些属性，例如高度集中的TF表示，信号重构和可接受的计算成本。在基本稀疏TF模型的基础上，我们首先使用加权策略有效地突出了TF脊，即使对于弱组分也是如此，然后应用快速迭代收缩阈值算法（FISTA）获得求解模型的有效数值逼近。此外，我们介绍了一种k稀疏性策略，用于自适应选择正则化参数。仿真研究表明，该方法不仅具有较高的能量集中度，而且在信号去噪方面也比其他标准TF方法具有更好的性能，特别是对于具有快速变化的IF的信号。两个真实的例子证实了该方法的潜力。