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# Fast directional weighted median filter for removal of random valued impulse noise

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### Fast directional weighted median filter for removal of random valued impulse noise

1. 1. • Motivations • Paper: Directional Weighted Median Filter • Paper: Fast Median Filters • Proposed Strategy • Simulation Results • Conclusion • References
2. 2. • The known median-based de-noising methods tend to work well for restoring the images corrupted by random-valued impulse noise with low noise level, but poorly for highly corrupted images [1]. • In Directional Weighted Median approach [1], standard Median filter is applied, which is not an efficient and effective method for calculating median value of a particular window.
3. 3. • In this approach, there are two major steps: 1. New Impulse Detector, which is based on the differences between the current pixel and its neighbors aligned with four main directions.
4. 4. • In this approach, there are two major steps: New Impulse Detector, which is based on the differences between the current pixel and its neighbors aligned with four main directions. 2. After detecting the impulse noise, we incorporate it with the Weighted Median Filter [3] to come up with new Directional Weighted Median Filter. 1.
5. 5. • New Impulse Detector 1. First, calculate the sum of all absolute differences of gray level values in a particular direction. Repeat it for all four directions using the following formula:
6. 6. • New Impulse Detector 2. Now the summation which is minimum from all four directions is used to detect whether the pixel is noisy or noise-free.
7. 7. • DWM Filter 1. We calculate the Standard Deviation of gray level values for all directions because it describes how tightly all the values are clustered around the mean in the set of pixels. where li,j shows that four pixels aligned with this direction are the closest to each other.
8. 8. • DWM Filter 2. We assign a weight to these pixels and restore the noisy pixel as: 3. Output of DWM Filter will be as follows:
9. 9. • Median filter, with its fine detail preservation and impulsive noise removal characteristics, has taken its place in many signal and image processing application. • But an important shortcoming of the median filter is that the median algorithm has low speed so as to restrict its application.
10. 10. Median Computation based on Histogram (MBH) • Considering that array values used for calculating median have limited distribution scope, denote the array for calculating median, where 0≤xi ≤M and xi is an integer. Our basic idea is to apply cut and try method from zero to M in turn till the median is found. In this way, the maximum number of times of experiments for searching median is M, that is to say the algorithm complexity is O(M).
11. 11. Median Computation based on Histogram and staged search (MBHSS) • In this extended version of the previous algorithm, the histogram is divided in equal chunks, • If the summation is smaller than the index of the middle value then we do not need to traverse that sub region for median , • Otherwise, the median value lies inside that region.
12. 12. Noisy image's pixel values for calculating median value, e.g. 5x5 window impulse detection using weighted difference along four directons in its neighborhood and threshold value determine direction on the basis of standard deviation and add pixel values to the window apply the fast median filter on the updated window and return the median value replace the central value of the considered window with median value
13. 13. • Standard Median Filter is very effective for impulse noise removal but it is inefficient because its time complexity is O(N2) or O(NlogN) and Fast median filter can be applied in linear time (i.e. O(M)). Simulation results shows that the time complexity of Directional Weighted Median Filter has been improved by incorporating the fast median filter.
14. 14. [1] Dong. Yiqiu, Xu. Shufang, “A New Directional Weighted Median Filter for Removal of Random Valued Impulse Noise” IEEE Signal Processing Letters. VOL. 14, No. 3, March 2007. [2] Tang. Quanhua, Zhou. Yan, Lei. Jine, “Fast median filters based on histogram and multilevel staged search”, IEEE Fourth International Conference on Image and Graphics, 2007.