Learning Structured Sparsity for Time-Frequency Reconstruction

Compressed sensing based algorithms are utilized to obtain high-resolution time-frequency distribution (TFD) with negligible cross-terms (CTs), however, performance deteriorates when the signal is composed of closely-located or overlapped components. Moreover, there is still an impressive resolution gap between obtained and ideal TFDs. Aiming at eliminating CTs meanwhile preserving resolution as high as possible in various hard cases, we propose a new U-Net aided iterative shrinkage-thresholding algorithm (U-ISTA), where unfolded ISTA with structure-aware thresholds is exploited to reconstruct near-ideal TFD. Specifically, we regard the U-Net as an adaptive threshold block, and structured sparsity of TFD is learned from numerous training data, thus underlying dependencies among neighboring time-frequency coefficients are incorporated into reconstruction. Experimental results over synthetic and real-life signals demonstrate that the proposed U-ISTA achieves superior performance compared with state-of-the-art algorithms.