It is about image de-noising methods and noise types

1. Presented By :
Haitham Abdel-atty Abdullah
Supervised By :
Prof .Dr . Mostafa Gadal-Haqq

2.  The process with which we reconstruct a signal from a
noisy one.
 Removing unwanted noise in order to restore the
original image.
 Method of estimating the unknown signal from
available noisy data”.

3.  Remove noise
 Preserve useful information
Image de-noising is an important pre-processing step for
image analysis.
Denoising

4. 𝑥𝑥
𝑛
𝑦 = 𝑥 + 𝑛
𝑛 = 𝑦 − 𝑥Noise

5. Additive Noise Model Multiplicative Noise Model
Noise signal gets added to the original
signal to produce a corrupted noisy signal.
Noise signal gets multiplied to the original
signal to produce a corrupted noisy signal.
The Additive noise model follows the
following rule:
The Multiplicative noise model follows
the following rule:

6. Gaussian Noise
 Is evenly distributed over the signal This means that each pixel in the
noisy image is the sum of the true pixel value and a random Gaussian
distributed noise value.

7. Impulse Noise
 The impulse noise is of two types, Fixed value and random value.
 Fixed value (salt and pepper noise)
 It is generally caused due to errors in transmission.
 It has only two possible values For an 8-bit image, the typical value for
pepper noise is 0 and for salt noise 255.
 The corrupted pixels are set alternatively to minimum or to maximum
values giving the image Salt and Pepper
 Random value
 The random valued impulse noise can have any value between 0 and 255
hence its removal is very difficult.

8. Uniform Noise
 The uniform noise cause by quantizing the pixels of image to a number
of distinct levels is known as quantization noise.
 Uniform noise can be analytically described by :

9. Periodic Noise
 Source: electrical or electromechanical interference during
image acquisition
 Easy to observe in frequency domain.
Image with periodic noise frequency domain

10. De-noising Methods
SPATIAL DOMAIN
LINEAR FILTERNON- LINEAR FILTER
FREQUENCY DOMAIN
Mean Filter
Weighted Mean Filter
Median Filter
LPF on Fourier Transform

11.  In spatial domain , we deal with images as it is (simply we directly deal
with the image matrix).

12.  Linear filters are used to remove certain type of noise.
 The linear filters work best with salt and pepper noise,
and Gaussian noise.
 Mean filters.
 Simple to design .
 These filters also
 tend to blur the sharp edges .
 destroy the lines and other fine details of image .

13.  One of the simplest spatial filtering operations.
 Replaces the centre value of the window with the
average values of its all nearest pixels values together
with itself.
 Advantage:
 Easy to implement
 Used to remove the impulse noise.
 Disadvantage:
 It does not preserve details of image. Some
details are removes of image with using the mean
filter.

14. 1/9
1/9
1/9
1/9
1/9
1/9
1/9
1/9
1/9
Origin x
y Image f (x, y)
New value = 1/9*106 + 1/9*104 +
1/9*100 + 1/9*108 +
1/9*99 + 1/9*98 +
1/9*95 + 1/9*90 + 1/9*85
= 98.3333
Filter
Simple 3*3
Neighbourhood
106
104
99
95
100 108
98
90 85
104 100 108
99 106 98
95 90 85
Original Image
Pixels
*
The above is repeated for every pixel in the
original image to generate the smoothed image

15. Extending border values outside with values at boundary.

16. (a) Original Image
(b) Image corrupted by Gaussian noise .
(c)De noising by mean filter

17.  Simple averaging (Mean filter) of neighboring pixels lead
to over-smoothing
 Instead of weighting all neighboring pixels equally, assign
higher weights to pixels that are closer to the pixel being
convolved.
Weighted Mean FilterMean Filter

18.  Can preserve edges .
 Very effective at removing impulsive noise .
 They are more powerful than linear filters because
they are able to reduce noise levels without blurring
edges.
 Difficult to design than linear filters.
 Median Filter.

19.  Median filter is one of the most important filters to remove
random valued impulse noise.
 In this filter the value of corrupted pixel in noisy image is
replaced by median value of corresponding window.
 The median is calculated by first sorting all the pixel
values into ascending order and then replace the pixel
being calculated with the middle pixel value
 Salt and pepper noise.

20. 99
Origin x
y Image f (x, y)
Sort the pixels values
106
104
99
95
100 108
98
90 85
104 100 108
99 106 98
95 90 85
Original Image Pixels
The above is repeated for every pixel in the
original image.
9985 104100 108989590 106

21. 21
Original
Salt & pepper
%20
Denoising by
Median filter
Original
Salt & pepper
%60
Denoising by
Median filter

22.  Frequency domain de-noising method is a kind of Transform Domain,
filtering where low pass filters (LPF.) is used by using Fast Fourier
Transform (FFT).
 The reason for doing the filtering in the frequency domain is generally
because it is computationally faster to perform two 2D Fourier
transforms and a filter multiply than to perform a convolution in the
image (spatial) domain.

23.  A low-pass filter attenuates high frequencies and retains low frequencies
unchanged.
 Here de-noising is done by designing a cut-off frequency .
 Convolution in the Spatial domain is equivalent to multiplication in the
frequency domain.
Original Image Fourier Transform Apply LPF on FT Inverse Fourier Transform

24. Original Image with noise Fourier Transform Inverse Fourier Transform

25. QUESTIONS ?
Be nice ...

26. Thank You