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Register a new userRobust Time-Frequency Reconstruction by Learning Structured Sparsity
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Added by
Haijian Zhang
Publication date
2020
fields
Electronic Engineering
and research's language is
English
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Time-frequency distributions (TFDs) play a vital role in providing descriptive analysis of non-stationary signals involved in realistic scenarios. It is well known that low time-frequency (TF) resolution and the emergency of cross-terms (CTs) are two main issues, which make it difficult to analyze and interpret practical signals using TFDs. In order to address these issues, we propose the U-Net aided iterative shrinkage-thresholding algorithm (U-ISTA) for reconstructing a near-ideal TFD by exploiting structured sparsity in signal TF domain. Specifically, the signal ambiguity function is firstly compressed, followed by unfolding the ISTA as a recurrent neural network. To consider continuously distributed characteristics of signals, a structured sparsity constraint is incorporated into the unfolded ISTA by regarding the U-Net as an adaptive threshold block, in which structure-aware thresholds are learned from enormous training data to exploit the underlying dependencies among neighboring TF coefficients. The proposed U-ISTA model is trained by both non-overlapped and overlapped synthetic signals including closely and far located non-stationary components. Experimental results demonstrate that the robust U-ISTA achieves superior performance compared with state-of-the-art algorithms, and gains a high TF resolution with CTs greatly eliminated even in low signal-to-noise ratio (SNR) environments.
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The design of high-resolution and cross-term (CT) free time-frequency distributions (TFDs) has been an open problem. Classical kernel based methods are limited by the trade-off between TFD resolution and CT suppression, even under optimally derived parameters. To break the current limitation, we propose a data-driven kernel learning model directly based on Wigner-Ville distribution (WVD). The proposed kernel learning based TFD (KL-TFD) model includes several stacked multi-channel learning convolutional kernels. Specifically, a skipping operator is utilized to maintain correct information transmission, and a weighted block is employed to exploit spatial and channel dependencies. These two designs simultaneously achieve high TFD resolution and CT elimination. Numerical experiments on both synthetic and real-world data confirm the superiority of the proposed KL-TFD over traditional kernel function methods.
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