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The module provides an introduction into the concepts of image restoration and filtering.

Image restoration

In many applications ( e.g. , satellite imaging, medical imaging, astronomical imaging, poor-qualityfamily portraits) the imaging system introduces a slight distortion. Often images are slightly blurred and imagerestoration aims at deblurring the image.

The blurring can usually be modeled as an LSI system with a given PSF h m n .

Fourier Transform (FT) relationship between the two functions.

The observed image is

g m n h m n f m n
G u v H u v F u v
F u v G u v H u v

Image blurring

Above we showed the equations for representing the common model for blurring an image. In we have an original image and a PSF function that we wish to apply to the image in order to model a basicblurred image.

Once we apply the PSF to the original image, we receive our blurred image that is shown in :

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Frequency domain analysis

looks at the original images in its typical form; however, it is often useful tolook at our images and PSF in the frequency domain. In , we take another look at the image blurring example above and look at how the imagesand results would appear in the frequency domain if we applied the fourier transforms.

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Source:  OpenStax, Intro to digital signal processing. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10203/1.4
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