Skip to content Skip to navigation

OpenStax-CNX

You are here: Home » Content » Image Restoration Basics

Navigation

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Image Restoration Basics

Module by: Robert Nowak. E-mail the author

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

Note: You are viewing an old version of this document. The latest version is available here.

Image Restoration

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

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

Figure 1: Fourier Transform (FT) relationship between the two functions.
Figure 1 (FT.png)

The observed image is

gmn=hmn*fmn g m n h m n f m n
(1)
Guv=HuvFuv G u v H u v F u v
(2)
Fuv=GuvHuv F u v G u v H u v
(3)

Example 1: Image Blurring

Above we showed the equations for representing the common model for blurring an image. In Figure 2 we have an original image and a PSF function that we wish to apply to the image in order to model a basic blurred image.

Figure 2
(a) (b)
Figure 2(a) (camera.png)Figure 2(b) (psf.png)

Once we apply the PSF to the original image, we receive our blurred image that is shown in Figure 3:

Figure 3
Figure 3 (cam_blur.png)

Frequency Domain Analysis

Example 1 looks at the original images in its typical form; however, it is often useful to look at our images and PSF in the frequency domain. In Figure 4, we take another look at the image blurring example above and look at how the images and results would appear in the frequency domain if we applied the fourier transforms.

Figure 4
Figure 4 (cam_freq.png)

Content actions

Download module as:

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks