This document discusses noise models and additive noise removal in digital image processing. It covers several types of noise that can affect images, including Gaussian, impulse, uniform, Rayleigh, gamma, exponential, and periodic noise. Various noise models are presented, such as definitions and equations for Gaussian, Rayleigh, gamma, exponential, uniform, and impulse noise. Examples of how different noise types affect images and histograms are also shown.

1. Digital Image Processing
Image Restoration
Noise models and additive noise removal
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 1

2. Image Restoration
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 2

3. Image Restoration
 What is noise (in the context of image processing) and how can it
be modeled?
 What are the main types of noise that may affect an image?
 What are the possible solutions?
 Subjective Vs Objective (Enhancement Vs Restoration)
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 3

4. Degradation Model for a Digital Image
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 4

5. Noise Models
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 5

6. Noise and Noise Models
 Gaussian (normal)
 Impulse (salt-and-pepper)
 Uniform
 Rayleigh
 Gamma (Erlang)
 Exponential
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 6

7. Effect of Noise on Images & Histograms
 Gaussian
 Exponential
 Impulse
(salt-and-pepper)
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 7

8. Effect of Noise on Images & Histograms
 Rayleigh
 Gamma (Erlang)
 Uniform
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 8

9. Noise Models: Gaussian Noise
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 9

10. Noise Models: Rayleigh Noise
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 10

11. Noise Models: Erlang (Gamma) Noise
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 11

12. Noise Models: Exponential Noise
Where
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 12

13. Noise Models: Uniform Noise
1 , if
  
 
0 otherwise
 
p ( z )
b a
a z b
The mean and variance are
given by



a b 2 b  a
, ( )
12

  
2
2

5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 13

14. Noise Models: Impulse (Salt and Pepper) Noise
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 14

15. Effect of Noise on Images & Histograms
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 15

16. Effect of Noise on Images & Histograms
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 16

17. Effect of Noise on Images & Histograms
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 17

18. Periodic Noise (Example)
 Spatially Dependent Case
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 18

19. Applicability of various noise models
5/13/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 19