  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.
