Optimal Sampling for Signal Restoration by Wiener Filter

A Wiener filter is a restoration filter that minimizes the mean square error (MSE) between original and the restored signal for given observation system. It has been observed that the minimum value of MSE by the Wiener filter still depends on the observation system, and it can further be reduced by selecting an appropriate observation system. In most general setting of signal processing, the observation system consists of an acquisition and a sampling process. Assuming an ideal acquisition process, we devise, in the paper, an optimal sampling scheme which further minimizes the MSE when used in conjunction with the Wiener filter. The optimum sampling uses the signal and the noise statistics in contrast to widely used regular sampling. It is shown that for correlated signal and noise, the proposed sampling significantly enhances the restoration capability of the filter, especially, for the case of low SNR and downsampling.