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## Removing Noise from Images

### Understanding Sources of Noise in Digital Images

Digital images are prone to a variety of types of noise. Noise is the result of errors in the image acquisition process that result in pixel values that do not reflect the true intensities of the real scene. There are several ways that noise can be introduced into an image, depending on how the image is created. For example:

• If the image is scanned from a photograph made on film, the film grain is a source of noise. Noise can also be the result of damage to the film, or be introduced by the scanner itself.

• If the image is acquired directly in a digital format, the mechanism for gathering the data (such as a CCD detector) can introduce noise.

• Electronic transmission of image data can introduce noise.

To simulate the effects of some of the problems listed above, the toolbox provides the imnoise function, which you can use to add various types of noise to an image. The examples in this section use this function.

### Removing Noise By Linear Filtering

You can use linear filtering to remove certain types of noise. Certain filters, such as averaging or Gaussian filters, are appropriate for this purpose. For example, an averaging filter is useful for removing grain noise from a photograph. Because each pixel gets set to the average of the pixels in its neighborhood, local variations caused by grain are reduced.

See Designing and Implementing Linear Filters in the Spatial Domain for more information about linear filtering using imfilter.

### Removing Noise By Median Filtering

Median filtering is similar to using an averaging filter, in that each output pixel is set to an average of the pixel values in the neighborhood of the corresponding input pixel. However, with median filtering, the value of an output pixel is determined by the median of the neighborhood pixels, rather than the mean. The median is much less sensitive than the mean to extreme values (called outliers). Median filtering is therefore better able to remove these outliers without reducing the sharpness of the image. The medfilt2 function implements median filtering.

 Note   Median filtering is a specific case of order-statistic filtering, also known as rank filtering. For information about order-statistic filtering, see the reference page for the ordfilt2 function.

The following example compares using an averaging filter and medfilt2 to remove salt and pepper noise. This type of noise consists of random pixels' being set to black or white (the extremes of the data range). In both cases the size of the neighborhood used for filtering is 3-by-3.

1. Read in the image and display it.

```I = imread('eight.tif');
imshow(I)```

```J = imnoise(I,'salt & pepper',0.02);
figure, imshow(J)```

3. Filter the noisy image with an averaging filter and display the results.

```K = filter2(fspecial('average',3),J)/255;
figure, imshow(K)```

4. Now use a median filter to filter the noisy image and display the results. Notice that medfilt2 does a better job of removing noise, with less blurring of edges.

```L = medfilt2(J,[3 3]);
figure, imshow(L)```

### Removing Noise By Adaptive Filtering

The wiener2 function applies a Wiener filter (a type of linear filter) to an image adaptively, tailoring itself to the local image variance. Where the variance is large, wiener2 performs little smoothing. Where the variance is small, wiener2 performs more smoothing.

This approach often produces better results than linear filtering. The adaptive filter is more selective than a comparable linear filter, preserving edges and other high-frequency parts of an image. In addition, there are no design tasks; the wiener2 function handles all preliminary computations and implements the filter for an input image. wiener2, however, does require more computation time than linear filtering.

wiener2 works best when the noise is constant-power ("white") additive noise, such as Gaussian noise. The example below applies wiener2 to an image of Saturn that has had Gaussian noise added.

1. Read in an image. Because the image is a truecolor image, the example converts it to grayscale.

```RGB = imread('saturn.png');
I = rgb2gray(RGB);```
2. The example then add Gaussian noise to the image and then displays the image. Because the image is quite large, the figure only shows a portion of the image.

```J = imnoise(I,'gaussian',0,0.025);
imshow(J)```

Portion of the Image with Added Gaussian Noise

3. Remove the noise, using the wiener2 function. Again, the figure only shows a portion of the image

```K = wiener2(J,[5 5]);
figure, imshow(K)```

Portion of the Image with Noise Removed by Wiener Filter