Image restoration is the process of recovering an image that has been degraded by some knowledge of degradation function * H *and the additive noise term . Thus in restoration, degradation is modelled and its inverse process is applied to recover the original image.

### Objective of image restoration:

The objective of image restoration is to obtain an estimate of the original image . Here, by some knowledge of * H *and , we find the appropriate restoration filters, so that output image is as close as original image as possible since it is practically not possible (or very difficult) to completely (or exactly) restore the original image.

Terminology:

- = degraded image
- = input or original image
- = recovered or restored image
- = additive noise term

##### In spatial domain:

where, represents convolution

##### In frequency domain:

After taking fourier transform of the above equation:

If the restoration filter applied is , then

(for restoration)

as restoration filter is the reverse of degration function and neglecting the noise term. Here, is linear and position invariant.