论文标题
“自通向器”过滤：数据驱动的确定性信号的反卷积
"Self-Wiener" Filtering: Data-Driven Deconvolution of Deterministic Signals
论文作者
论文摘要
我们考虑了强大的反卷积的问题，尤其是恢复未知的确定性信号，与已知的过滤器卷曲并被加性噪声损坏。我们提出了一种新颖的，非辅助数据驱动的方法。具体而言，我们的算法在频域中起作用，在频域中，它试图模仿最佳无法实现的非线性Wiener样滤波器，就好像已知未知确定性信号一样。这导致阈值型正则化估计器，其中每个频率处的阈值以数据驱动方式确定。我们对我们提出的估计器进行理论分析，并在低和高信噪比（SNR）方面得出其平方误差（MSE）的近似公式。我们表明，在低SNR制度中，我们的方法提供了增强的噪声抑制作用，在高SNR方向上，它接近了最佳的无法实现的解决方案。此外，正如我们在模拟中所证明的那样，我们的解决方案非常适合（大约）带限制或频域稀疏信号，并相对于所得MSE中的其他方法提供了几个DBS的显着增益。
We consider the problem of robust deconvolution, and particularly the recovery of an unknown deterministic signal convolved with a known filter and corrupted by additive noise. We present a novel, non-iterative data-driven approach. Specifically, our algorithm works in the frequency-domain, where it tries to mimic the optimal unrealizable non-linear Wiener-like filter as if the unknown deterministic signal were known. This leads to a threshold-type regularized estimator, where the threshold at each frequency is determined in a data-driven manner. We perform a theoretical analysis of our proposed estimator, and derive approximate formulas for its Mean Squared Error (MSE) at both low and high Signal-to-Noise Ratio (SNR) regimes. We show that in the low SNR regime our method provides enhanced noise suppression, and in the high SNR regime it approaches the optimal unrealizable solution. Further, as we demonstrate in simulations, our solution is highly suitable for (approximately) bandlimited or frequency-domain sparse signals, and provides a significant gain of several dBs relative to other methods in the resulting MSE.
