Self-Wiener Filtering: Data-Driven Deconvolution of Deterministic Signals

We consider the problem of robust deconvolution, and particularly recovery an unknown deterministic signal convolved with a known filter corrupted by additive noise. present novel, non-iterative data-driven approach. Specifically, our algorithm works in frequency-domain, where it tries to mimic optimal unrealizable non-linear Wiener-like as if were known. This leads threshold-type regularized estimator, threshold at each frequency is determined manner. perform theoretical analysis proposed derive approximate formulas for its Mean Squared Error (MSE) both low high Signal-to-Noise Ratio (SNR) regimes. show that SNR regime method provides enhanced noise suppression, approaches solution. Further, we demonstrate simulations, solution highly suitable (approximately) bandlimited or frequency-domain sparse signals, significant gain several dBs relative other methods resulting MSE.