1. 23 November 20151 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.

2. 23 November 20152 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 : LennaCorrupted Lenna

3. 23 November 20153 Types of noise 1. Dependent Noise (Gaussian Noise) 2. Independent Noise (Salt and Pepper Noise) Various ways of Classification. Two general cases :

4. 23 November 20154 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. One kind of random noise, appearing on the image as additive random impulsive dots or small regions. We Address here:

5. 23 November 20155 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. Simulated noisy images satisfying our assumptions

6. 23 November 20156 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.

7. 23 November 20157 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)

8. 23 November 20158 Basic Idea of Noise Detection Each window verdicts about each of the s 2 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

9. 23 November 20159 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 40525558 60629060 5706058 55616425 52565963 50545861 48525659 46505457 12445 108321 431841 9111032 Good Pixel Corrupt Pixel δ = 25

10. 23 November 201510 Combining Local Solutions Each non-boundary pixel examined by S 2 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.

11. 23 November 201511 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.

12. 23 November 201512 Combining Local Solutions Threshold Ratio, φ Minimum ratio of accepted verdicts needed for a pixel to be declared uncorrupted globally. Two Threshold ratios : Decision Tree

13. 23 November 201513 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.

14. 23 November 201514 Noise Detection Simulation Classification Efficiency, Error Detection Efficiency,

15. 23 November 201515 Effect of Deviation Parameter φ e = 0.7 and φ n = 0.85, ρ = 0.34, Ω = 0.5, s = 4

16. 23 November 201516 Effect of Density Parameter For noise density 30% optimal value of ρ is 0.4 as depicted

17. 23 November 201517 Effect of Threshold ratio : For ρ = 0.4, Ω = 0.5, s=4, Noise Density = 30%, optimal value of φ e = 0.7 and φ n = 0.85.

18. 23 November 201518 Various noise distribution.

19. 23 November 201519 Noise Filtering Performance Peak Signal to Noise Ratio vs. Noise Density

20. 23 November 201520 12 % Noise PSNR = 30 dB 30 % Noise, PSNR = 26 dB 6 % Noise PSNR = 32 dB Visualization

21. 23 November 201521 Total Cost : O((m-s+1)(n-s+1)s 2 + mn + ρs 2 (m-s+1)(n-s+1)+mn) = O(mns 2 (1+ρ)) Number of windows = Cost per window for Local classification: O(s 2 ) Time for Global Error Classification : O(mn) Filtering : O(ρs 2 ) per window Final Estimation : O(mn) Complexity

22. 23 November 201522 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.

23. 23 November 201523 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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