Md. Tanvir Al Amin (Presenter)
tanviralamin@gmail.com
Anupam Bhattacharjee
abrbuet@yahoo.com
Department of Computer Science and Engineering,
Bangladesh University of Engineering and Technology,
Dhaka, Bangladesh.
13 April 2015
1
What we consider Noise
Presence of unwanted components in a signal.
Inherent with Signal Handling devices.
In case of a digital image, noise is deviation of
image pixels from their actual values.
Standard Image : Lenna
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Corrupted Lenna
2
Types of noise
Various ways of Classification.
Two general cases :
1. Dependent Noise (Gaussian Noise)
2. Independent Noise (Salt and Pepper Noise)
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3
Noise Reduction Problem
It is clear that we need to remove noise.
But we can only reduce it.
An ill posed problem since
Not well defined whether a pixel is
corrupted or not.
We Address here:
One kind of random noise, appearing on the
image as additive random impulsive dots or
small regions.
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Our Assumptions
1. Impulsive Noise is uniformly distributed
throughout the whole image having fixed noise
density.
2. Natural Images have continuous tones.
Noisy pixels vary more than a threshold value.
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Simulated noisy images satisfying our assumptions
5
Stages of the Solution
Stage 1 :
Detect the pixels which are corrupted.
Stage 2 :
Keep the uncorrupted pixels intact.
Estimate values for the corrupted pixels from
its neighboring good pixels.
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Basic Idea of Noise Detection
Take window of certain dimension s, depending on
Noise Density ρ
Sweep it for all possible positions in the image array.
Process Each window.
A window
starting
at (2,3)
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Basic Idea of Noise Detection
Each window verdicts about each of the s2 pixels
inside, whether it is Corrupted or not.
Local Classification : Classification of each pixel by a
single window.
Global Classification : Combined output of all Local
Decision
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Processing Each Window
Fit a plane with the pixel
values in a window
(Least Squares Regression)
Let Z be plane approximation
Select those pixels as
corrupted for which deviation
exceeds Parameter δ
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52
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62
90
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5
70
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61
64
25
52
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12
4
4
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10
8
32
1
43
18
4
1
9
11
10
32
δ = 25
Good
Pixel
Corrupt
Pixel
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Combining Local Solutions
Each non-boundary pixel examined by S2 windows.
Local Classifications are combined by “Majority
vote”.
Verdicts of each window considered as “votes”.
Idea is : if most of the windows report a pixel
“uncorrupted”, It is highly probable that this pixel is
actually uncorrupted.
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Combining Local Solutions
To discriminate between edge and noise we
introduce, Classifier Parameter Ω
= Ratio of successful judgments needed for any
pixel to be flat
We assume : In case of high contrast grainy
parts or for edge pixels, large number of pixels
inside a window will be reported wrong, causing
judgment of that window unreliable.
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Combining Local Solutions
Threshold Ratio, φ
Minimum ratio of accepted
verdicts needed for a pixel to
be declared uncorrupted
globally.
Two Threshold ratios :
 n : used for flat or non grainyregions
 e : used for edge pixel or grainypart
Decision Tree
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Noise Filtering
Fit a paraboloid with the good
pixel values in each window
From Paraboloid Approximation,
Find suggestion for each
corrupted pixel
Globally Estimate value of a
noisy pixel by averaging all
suggestions.
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In case there is
no estimate
about a pixel,
we use pixel
averaging for it.
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Noise Detection Simulation
Classification Efficiency,

Number of Pixelsclassifiedcorrectly
100%
Total number of Pixelsin theimage
Error Detection Efficiency,
Number of corruptedpixelscorrectlydetected

100%
Total number of corruptedpixels
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Effect of Deviation Parameter
95
90
90
Detection Efficiency (%)
Classification Efficiency (%)
100
85
80
75
80
70
60
50
40
30
20
10
70
0
10
20
30
40
Deviation parameter δ
50
60
0
0
10
20
30
40
50
60
Deviation parameter δ
φe = 0.7 and φn = 0.85, ρ = 0.34, Ω = 0.5, s = 4
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Effect of Density Parameter
100
90
80
% Efficiency
70
60
50
40
30
20
Classification efficiency
Detection efficiency
10
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Density Parameter ρ
1
For noise density 30% optimal value of ρ is 0.4 as depicted
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Effect of Threshold ratio :
For ρ = 0.4, Ω = 0.5, s=4, Noise Density = 30%, optimal value of
φe = 0.7 and φn = 0.85.
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Various noise distribution.
100
90
90
80
Detection Efficiency (%)
Classification Efficiency (%)
100
70
60
50
40
30
20
10
80
70
60
50
40
30
20
10
0
0
10
20
30
40
Noise Density (% )
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50
60
0
0
10
20
30
40
50
60
Noise Density (% )
18
Noise Filtering Performance
35
PSNR (dB)
30
25
20
15
10
5
0
0%
10%
20%
30%
40%
Noise Density (%)
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Peak Signal to Noise Ratio vs. Noise Density
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Visualization
6 % Noise PSNR = 32 dB
30 % Noise, PSNR = 26 dB
12 % Noise PSNR = 30 dB
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Complexity
Number of windows = (m  s  1)(n  s  1)
Cost per window for Local classification: O(s2)
Time for Global Error Classification : O(mn)
Filtering : O(ρs2) per window
Final Estimation : O(mn)
Total Cost :
O((m-s+1)(n-s+1)s2 + mn + ρs2(m-s+1)(n-s+1)+mn)
= O(mns2(1+ρ))
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Success
No Blind mean or median filtering.
Output doesn’t suffer from unwanted loss in sharpness.
Main operations are solving systems of linear equations.
No complicated mathematical operations or transformation.
Specialized data structure is not necessary.
Implementation logic is easy and economical with
resources.
We get more than 92% success on average.
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Shortcomings
Noise detection is done in single pass,
Filtering is also done in another single pas.
Multilevel detection and filtering would improve it.
For Regression, L1 norm is used.
Less calculation needed  results in less accuracy.
Only concentrates in algebraic methods considered.
Considering frequency information and wavelet based
statistics along with, would yield better result in
noise detection and removal
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