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## What is Wiener filtering in image processing?

There is a technique known as Wiener filtering that is used in image restoration. This technique assumes that if noise is present in the system, then it is considered to be additive white Gaussian noise (AWGN). The inverse filter of a blurred image is a highpass filter.

## What is the use of Wiener filter?

In signal processing, the Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed noisy process, assuming known stationary signal and noise spectra, and additive noise.

**How to implement the Wiener filter in practice?**

To implement the Wiener filter in practice we have to estimate the power spectra of the original image and the additive noise. For white additive noise the power spectrum is equal to the variance of the noise. To estimate the power spectrum of the original image many methods can be used.

### How is Wiener filtering used in image restoration?

To illustrate the Wiener filtering in image restoration we use the standard 256×256 Lena test image. We blur the image with the lowpass filter then put into the blurred image the additive white Gaussian noise of variance 100. The Wiener filtering is applied to the image with a cascade implementation of the noise smoothing and inverse filtering.

### How is the Wiener filter used in MSE?

• 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). • Wiener filters are often applied in the frequency domain.

**Which is better Wiener filtering or noise smoothing?**

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.