April 22, 2023 1

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.

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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)

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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 5860 62 90 605 70 60 5855 61 64 25

52 56 59 6350 54 58 6148 52 56 5946 50 54 57

12 4 4 510 8 32 143 18 4 1

9 11 10 32

Good Pixel

Corrupt Pixel

δ = 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 FilteringFit a paraboloid with the good pixel values in each window

From Paraboloid Approximation,Find suggestion for each corrupted pixelGlobally 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.

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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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0 10 20 30 40 50 60Noise Density (%)

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Noise Filtering Performance

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Noise Density (%)

PSN

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B)

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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SuccessNo 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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