Basic Questions on Wiener Filtering

1. What is the main objective of a Wiener filter?
2. Why Wiener filter is called optimal filter?
3. What type of filter is Wiener filter?
4. Under what condition Wiener filtering will become inverse filtering?

What is the main objective of a Wiener filter?

Description. The goal of the Wiener filter is to compute a statistical estimate of an unknown signal using a related signal as an input and filtering that known signal to produce the estimate as an output.

Why Wiener filter is called optimal filter?

The Wiener filtering is optimal in terms of the mean square error. In other words, it minimizes the overall mean square error in the process of inverse filtering and noise smoothing.

What type of filter is Wiener filter?

The Wiener filter is the MSE-optimal stationary linear filter for images degraded by additive noise and blurring. Calculation of the Wiener filter requires the assumption that the signal and noise processes are second-order stationary (in the random process sense).

Under what condition Wiener filtering will become inverse filtering?

Note that at spatial frequencies where the signal-to-noise is very high, the ratio R_N(u, υ)/ R_I(u, υ) approaches zero, and the Wiener filter reduces to the inverse filter. However, when the signal-to-noise ratio is very poor (i.e., R_N(u, υ)/ R_I(u, υ) is large), the estimated spatial frequencies approach zero.