23 november 20151 md. tanvir al amin (presenter) [email protected] anupam bhattacharjee...
TRANSCRIPT
April 20, 2023 1
Md. Tanvir Al Amin (Presenter)[email protected]
Anupam Bhattacharjee [email protected]
Department of Computer Science and Engineering,Bangladesh University of Engineering and Technology,
Dhaka, Bangladesh.
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Presence of unwanted components in a signal.Inherent with Signal Handling devices.
What we consider Noise
In case of a digital image, noise is deviation of image pixels from their actual values.
Standard Image : Lenna Corrupted Lenna
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Types of noise
1. Dependent Noise (Gaussian Noise)1. Dependent Noise (Gaussian Noise)
2. Independent Noise (Salt and Pepper Noise)2. Independent Noise (Salt and Pepper Noise)
Various ways of Classification.
Two general cases :
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Noise Reduction ProblemIt is clear that we need to remove noise.It is clear that we need to remove noise.But we can only reduce it.But we can only reduce it.
An ill posed problem sinceAn ill posed problem since Not well defined whether a pixel is Not well defined whether a pixel is corrupted or notcorrupted or not..
One kind of random noise, appearing on the image as additive random impulsive dots or small regions.
We Address here:
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Our Assumptions1. 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.
Simulated noisy images satisfying our assumptions
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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)
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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Fit a plane with the pixel values in a window(Least Squares Regression)
Processing Each Window
Let Z be plane approximation
Select those pixels as corrupted for which deviation exceeds Parameter δ
40 52 55 58
60 62 90 60
5 70 60 58
55 61 64 25
52 56 59 63
50 54 58 61
48 52 56 59
46 50 54 57
12 4 4 5
10 8 32 1
43 18 4 1
9 11 10 32
Good Pixel
Good Pixel
Corrupt Pixel
Corrupt Pixel
δ = 25δ = 25
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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 SolutionsTo 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
partgrainy or pixel edgefor used:eregionsgrainy non or flat for used:n
Threshold Ratio, φ Minimum ratio of accepted verdicts needed for a pixel to be declared uncorrupted globally.
Two Threshold ratios :
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.
In case there is no estimate about a pixel, we use pixel averaging for it.
In case there is no estimate about a pixel, we use pixel averaging for it.
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Noise Detection Simulation
Classification Efficiency,
%100image in the Pixels ofnumber Total
correctly classified Pixels ofNumber
Error Detection Efficiency,
%100pixels corrupted ofnumber Total
detectedcorrectly pixels corrupted ofNumber
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Effect of Deviation Parameter
φe = 0.7 and φn = 0.85, ρ = 0.34, Ω = 0.5, s = 4
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Deviation parameter δ
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Deviation parameter δ
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Effect of Density Parameter
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Density Parameter ρ
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Classification efficiencyDetection efficiency
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.
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Noise Density (%)
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Noise Density (%)
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Noise Filtering Performance
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Noise Density (%)
PS
NR
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Peak Signal to Noise Ratio vs. Noise Density
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12 % Noise PSNR = 30 dB
30 % Noise, PSNR = 26 dB 6 % Noise PSNR = 32 dB
Visualization
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Total Cost : O((m-s+1)(n-s+1)s2 + mn + ρs2(m-s+1)(n-s+1)+mn)
= O(mns2(1+ρ))
Number of windows = )1)(1( snsm
Cost per window for Local classification: O(s2)Time for Global Error Classification : O(mn)Filtering : O(ρs2) per windowFinal Estimation : O(mn)
Complexity
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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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