Example: Wiener Filtering

Functions > Image Processing > Convolution and Filters > Example: Wiener Filtering

Use the wiener2d function to reduce additive random noise in images.

Wiener filtering was one of the first methods developed to reduce additive random noise in images. It works on the assumption that additive noise is a stationary random process, independent of pixel location; the algorithm minimizes the square error between the original and reconstructed images.

For information on using this example, refer to About Image Processing Examples.

Using Random Uniform Distribution Noise

1. Create a simple rectangular box image

2. Add noise to the box image.

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      <apply>
        <indexer />
        <id xml:space="preserve" label-is-contextual="true" label="Variable">noise</id>
        <apply>
          <plus />
          <apply>
            <mult />
            <id xml:space="preserve">i</id>
            <real>100</real>
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          <id xml:space="preserve">j</id>
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    <resultFormat>
      <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
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3. Use a 7 x 7 window Wiener filter on the image.

4. Scale and display the two images:


(wiener_sl.bmp)	(wiener_sf77.bmp)

The outlines of the square have not been blurred, but the noise has been smoothed. However, the noise is not filtered out near the square outlines for a neighborhood the size of the filtering window.

5. Use a 3 x 3 window on the image.


(wiener_sf33.bmp)

In this image, there is less overall smoothing, but it extends nearer to the square outlines.

Using Gaussian Noise

1. Read in an image file and degrade it by random white Gaussian noise.

2. Add Gaussian noise to the image.

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      </apply>
      <apply>
        <indexer />
        <id xml:space="preserve" label-is-contextual="true" label="Variable">noise</id>
        <apply>
          <plus />
          <apply>
            <mult />
            <id xml:space="preserve">i</id>
            <apply>
              <id xml:space="preserve" label-is-contextual="true" label="Function">cols</id>
              <id xml:space="preserve" label-is-contextual="true" label="Variable">M</id>
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          <id xml:space="preserve">j</id>
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(fruit_sm.bmp)	(fruit_sl.bmp)

3. Suppress the noise using Wiener filtering with a 5 x 5 window.


(fruit_w55.bmp)