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# Wiener Filtering

[Laboratory]

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). Wiener filtering normally requires a priori knowlegde of the power spectra of the noise and the original image. What if the spectral density functions of the image and noise are unknown? In this case, we use a parametric version of the Wiener filter. A simplified equation of the Wiener filter R(u) is given below for the 1D case.

The inverse filter of a blurred image is a highpass filter. The parameter K of the Wiener filter is related to the low frequency aspect of the Wiener filter. The Wiener filter behaves as a as a bandpass filter, where the highpass filter is due to the inverse filter and the lowpass filter to the parameter K. Observe that when K=0, the Wiener filter becomes the inverse filter.

The degraded image for our experiment is shown below.

a)blurred byte type image; b)its spectrum
a) | b)

a)frequency response of the Wiener filter; b)spectrum of the Wiener filtered image
a) | b)

The result of the Wiener filtering operation is depicted below.

a)Wiener filter restored image; b)original image
a) | b)

- Lab: Wiener Filtering