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| ARTICLE |
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| Year : 2010 | Volume
: 56
| Issue : 4 | Page : 219-226 |
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Efficient Median Filter for Restoration of Image and Video Sequences Corrupted by Impulsive Noise
T Ravi Kishore1, K Deergha Rao2
1 Defence Electronics Research Laboratory, Hyderabad, India
2 R and T Unit for Navigational Electronics, Osmania University, Hyderabad, India
| Date of Web Publication | 24-Sep-2010 |
Correspondence Address:
T Ravi Kishore
Defence Electronics Research Laboratory, Hyderabad
India
 DOI: 10.4103/0377-2063.70645
 Abstract | | |
Various switching-based median filters have been proposed in the literature for restoration of extremely corrupted images and video sequences by impulsive noise. Among these, switching median filters with boundary discriminative noise detection (BDND) are very effective and outperform all the previously proposed median-based filters. However, the calculation is very time-consuming. Hence, in this paper, a median filter with an efficient BDND (EBDND) is proposed for denoizing image and video sequences corrupted by impulsive noise. The proposed EBDND uses a faster sorting algorithm both in noise detection and adaptive filtering stages for the restoration of image and video sequences contaminated by impulse noise. For motion estimation of the video sequence, block-matching technique is used. The performance of the proposed EBDND is demonstrated through computer simulations in comparison with the BDND method. Keywords: Image denoizing, Impulse noise detection, Nonlinear filter, Median filter
How to cite this article:
Kishore T R, Rao K D. Efficient Median Filter for Restoration of Image and Video Sequences Corrupted by Impulsive Noise. IETE J Res 2010;56:219-26 |
| 1. Introduction | |  |
Many types of image and video degradations produced both during acquisition and transmission are due to impulsive noise contamination. Hence, suppression of impulsive noise is one of the important tasks in image and video restoration. Several nonlinear filters have been proposed for the restoration of video sequences contaminated by impulsive noise. Among these, the median filters and their variants can be considered as the most popular types used for impulsive noise suppression [1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11] . Their fundamental advantage is that they can suppress the impulsive noise (also known as the salt and pepper noise) without edge blurring. Conventional median filtering approaches apply the median operation to each pixel unconditionally without identifying whether a pixel is "corrupted" or "uncorrupted" which would inevitably alter the intensities and remove signal details of those uncorrupted pixels. Therefore, a noise detection process to discriminate the uncorrupted pixels from the corrupted ones prior to applying nonlinear filtering is highly desirable. The switching median filters [12],[13],[14],[15],[16],[17],[18],[19] had shown significant performance improvement.
Florencio and Schafer [12] have proposed a switching-based median filtering methodology by applying "no filtering" to preserve true pixels and standard median (SM) filter to remove impulse noise. But this method is nonadaptive to a given, but unknown, noise density and is prone to yield pixel misclassifications, especially at higher noise densities. The noise adaptive soft-switching median (NASM) filter was proposed in [16] to address this issue. The NASM achieves robust performance in removing impulse noise when the noise ranges from 10 to 50%. However, for the restoration of video sequences corrupted with noise density greater than 50%, the quality of the recovered sequences becomes significantly degraded. Pei-Eng Ng and Kai-Kuang proposed highly accurate noise detection algorithm boundary discriminative noise detection (BDND) [19] . The BDND can achieve pleasing results even if the noise density is 90%. But it is too time consuming to be used in real time applications. This paper proposes a median filter with an efficient BDND (EBDND) for restoration of images and motion compensated median filter with EBDND for restoration of video sequences contaminated by the impulsive noise. The proposed EBDND reduces the processing time of BDND by using a new sorting technique. Also, the proposed EBDND can achieve a higher peak signal-to-noise ratio (PSNR) in restoring noisy images or video sequences by using improved adaptive filtering stage, while being much less time-demanding, compared with the BDND method. The proposed median filtering with EBDND is applied on the first frame of the sequence; the consecutive frames are restored using motion compensated median filter with EBDND. The fast block matching method in [20] is used for motion estimation.
| 2. Impulse Noise Detection | | |
The proposed median filter with EBDND is applied to each pixel of the noisy image in order to identify whether the pixel is "corrupted" or "uncorrupted". After such an application to the entire image, a two-dimensional binary decision map is formed at the end of the noise detection stage, with "0s" indicating the positions of "uncorrupted" pixels and "1s" for those of the "corrupted" ones. To accomplish this objective, all the pixels within a pre-defined window that is centered on the considered pixel are grouped into three clusters: low-intensity cluster, medium-intensity cluster and high-intensity cluster. The current pixel is identified as "uncorrupted," only if it falls into the medium-intensity cluster; otherwise, it is assigned as corrupted. Consider an M × N size and L gray level image to be processed. The first iteration employs a window of size 21 × 21, instead of using quick sort algorithm to sort the pixels of local window as in BDND. A new sorting method is used to sort the pixels in the noise detection and adaptation stages. The steps of the first iteration are as follows.
2.1 New Sorting Technique
Step 1: Impose a local window of size 21 × 21, which is centered on the current pixel.
Step 2a: Sort the pixels in the window (W) in ascending order, using the following new sorting method and find the median, med, of the sorted vector.
Initialize an array A[n] with zeros, where n = 0, 1, 2,…,L - 1.
for i ← 1 to 21, do
for j ← 1 to 21, do
A[W(i,j)] = A[W(i,j)] + 1
end
end
For all A[n]≠0, V[] = value n occurring A[n] times, where A[n] implies pixel value n occurring A[n] times. V is the sorted vector of length 441.
Step 2b: For odd numbered column, subtract first row pixels of the previous window W from A[n] and add last row pixels of the present window W to A[n].
For even numbered column, add first row pixels of the present window W to A[n] and subtract last row pixels of the previous window W from A[n].
Whenever boundary of the image is reached, then subtract first column pixels of the previous window W from A[n] and add last column pixels of the present window W to A[n].
For all A[n] ≠ 0, V [] = value n occurring A[n] times, where A[n] implies pixel value n occurring A[I] times. V is the sorted vector of length 441.
Step 3: Compute the intensity difference between each pair of adjacent pixels across the sorted vector and obtain the difference vector.
Step 4: For the pixel intensities between 0 and med in the sorted vector, find the maximum intensity difference in the difference vector of the same range and mark its corresponding pixel in the sorted vector as boundary b1.
Step 5: Likewise, boundary b2 is identified for pixel intensities between med and 255; three clusters are thus formed.
Step 6: If the pixel belongs to the medium cluster, it is classified as "uncorrupted" pixel and the classification process stops for the current pixel; else, the second iteration will be invoked as shown in Steps 7 and 8.
Step 7: Impose a 3 × 3 window, being centered on the concerned pixel and repeat Steps 2-5.
Step 8: If the pixel under consideration belongs to the medium cluster, it is classified as "uncorrupted", or else as "corrupted".
Once the classification of current pixel is completed, the remaining pixels in odd numbered column are classified by shifting window one pixel downward and employing steps 2b-8 until boundary of the image is reached. When the boundary of the image is reached, the window is shifted right by one pixel and steps 2b-8 are employed. Whereas pixels in the even numbered column are classified by shifting window one pixel upward and following steps 2b-8. It should be noted that for the first window step 2a is used, whereas for all other cases, step 2b is used. For the understanding of the algorithmic steps mentioned above, a 5 × 5 (instead of 21 × 21) windowed sub-image with the center pixel "60" (being boxed) is used as an example for illustrating the proposed process as shown in [Figure 1].
Current pixel is 60, {A[0] = 8, A(32) = 3, A(39) = 1, A(41) = 1, A(47) = 2, A(60) = 2, A(65) = 1, A(255) = 7}. Therefore, the sorted vector V0 is {0, 0, 0, 0, 0, 0, 0, 0, 32, 32, 32, 39, 41, 47, 47, 60, 60, 65, 255, 255, 255, 255, 255, 255, 255} and median value (med) is 41.
The vector of intensity differences between each pair of two adjacent pixels in V0 is computed as Vd: Vd={0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 7, 2, 6, 0, 13, 0, 5, 190, 0, 0, 0, 0, 0, 0}. For the pixels with intensities between 0 and med in the V0, the corresponding maximum difference in the vector Vd is 32, which is the difference between the pixel intensities 0 and 32.
For the pixels with intensities between med and 255 in the V0, the maximum difference in the vector Vd is 190, which is the difference between the pixel intensities 65 and 255. Hence, b1 = 0 and b2 = 65. Thus, the lower intensity cluster is {0, 0, 0, 0, 0, 0, 0, 0}, medium-intensity cluster is {32, 32, 32, 39, 41, 47, 47, 60, 60, 65}, and the higher intensity cluster is {255, 255, 255, 255, 255, 255, 255}.
Since the center pixel "60" belongs to the medium intensity cluster, the current pixel is identified as "uncorrupted" and the second iteration need not to be invoked. Local window slides down by one row and the current pixel become 255. Pixels {41, 0, 0, 39, 255} move out of the local window and {255, 255, 0, 60, 47} move into the local window. Counting array can be updated simply by subtracting those pixels just moved out and adding those pixels that just moved into the window. Then repeat the above process to decide if the current pixel is corrupted or uncorrupted. If a pixel is not classified as "uncorrupted", second iteration will be invoked with a window size of 3×3 and steps 2-5 are repeated. If the pixel under consideration belongs to the medium cluster, it is classified as "uncorrupted", otherwise as "corrupted".
| 3. Adaptive Filtering Scheme | | |
The major contributions of making the entire switching median filter being noise-adaptive come from the impulse-noise detection as described in the previous section. Based on the binary decision map, "no filtering" is applied to those "uncorrupted" pixels, while the proposed sorting method with an adaptively determined window size WF×WF is applied to each "corrupted" one.
In the BDND method, starting with WF = 3, the filtering window iteratively extends outward by one pixel in all the four sides of the window, provided the number of uncorrupted pixels is less than half of the total number of pixels (Sin) within the filtering window. While WF < WD (where WD is the maximum window size [5] ) or number of uncorrupted pixels is equal to zero. At high noise-density ( > 50%), the number of uncorrupted pixels in a square is often less than Sin and window size will almost increase until it reaches the maximum window size WD; this results in blurring image detail severely.
In the proposed EBDND method, filtering starts with window size WF = 3. The filtering window extends outward by one pixel in all the four sides of the window, if the number of uncorrupted pixels is equal to 0. Otherwise, the corrupted pixel is replaced with the median of the uncorrupted pixels within the filtering window. If the number of uncorrupted pixels in filter window exceeds 0, the extension is stopped. Thus, the maximum window size for the EBDND method is 5, even if the noise density level is 90%.
Suppose exploiting switch median filter to a noise pixel xi,j and the finally decided window size is WF, the output pixel yi,j is:
yi,j = median {xi + s,j + k / − (WF - 1)/2 ≤ s, k ≤ (WF - 1)/2}
In the median filtering process, those corrupted pixels are excluded and only uncorrupted ones are considered to get median value. Median is calculated using proposed sorting method.
| 4. Motion Compensated Median Filtering | | |
In the majority of cases, TV pictures contain the same objects but displaced (moving) from one frame to the next. In motion compensated filtering, the frame-to-frame displacements of different objects are estimated, and the EBDND method is applied on the displaced previous frame elements. Since the block matching is a widely used method for video compression and many fast algorithms for block matching exist in the literature [20] , for estimation of the displaced previous elements, block-matching motion estimation is used in the motion compensated median filtering.
| 5. Computational Complexity | | |
The EBDND and motion compensated median filter have both noise detection stage and noise filtering stage as described in the above sections. In the filtering process, if the number of uncorrupted pixels in filter window exceeds zero, the extension is stopped. So, most of the finally decided window size WF will not be larger than 5, even if the noise density level is 90%. Consider an M × N size and L gray level image to be processed, the first iteration of our noise detection process uses a 21 × 21 window. The local window sliding from top to bottom, slides to right by one column and proceeds from bottom to top of the image considered. At the beginning of each row, sorting of gray levels in the sliding window is computed. This needs 21 × 21 = 441 times integer plus operations. When the filtering window slides to the next row, the array A is updated by 21 times minus operations and 21 times plus operations, the process is repeated until the center pixel of the sliding window reaches bottom boundary of the image. Then, sliding window slides to right by one column and proceeds to the top of the image until center pixel of the sliding window reaches top boundary of the image. If we do not distinguish minus operation and plus operation, then the total computation of sorting pass the whole image is (441 × 1) + 42 × (M - 1) × N times plus operations [achieving a time complexity of O (2N) , where N = 21].
The sorted vector has 441 elements. For each pixel, at the most 440 minus operations are needed to compute difference vector. Then two boundaries b1 and b2 are obtained to decide if the pixel is corrupted or not. The computation for the first iteration is approximated as K M × N times integer operations, where k = 484 (best case time complexity).
The second iteration of our noise detection process uses 3 × 3 sliding window, so only 9 times integer plus operations and 8 times minus operations are needed to sort the pixels and find intensity differences, respectively, for each identified "corrupted" pixel in the first iteration. The second iteration needs 17 × M × N times integer operations in the worst-case scenario. Together, the detection process is less than 501 times integer plus operations for each pixel (worst case time complexity).
The BDND noise detection method also employs a sliding window of size 21 × 21; pixels in the window are sorted in ascending order and the median found. Then compute the intensity difference between each pair of adjacent pixels, find the maximum difference in the range between 0 and median, the corresponding intensity is the boundary b1 . Similarly, the boundary b2 is identified for pixel intensity between median and 255. If the pixel intensity is greater than b1 and lesser than b2 , it is identified as "uncorrupted". If the pixel is classified as "corrupted", then the second iteration will be invoked by the same procedure as in the first iteration except using a 3 × 3 window. There are 441 pixels in a window of size 21 × 21 in the first iteration; so, for each pixel, 440 minus operations are needed to compute the difference of each pair of adjacent pixels across sorted vector. Majority of the computation of the BDND method consists in the first iteration, where sorting operation is very time consuming. Quick sort algorithm is widely used and the performance is really good. So, quick sort algorithm is used to fulfill the BDND method and compare with our EBDND method. The time complexity of quick sort algorithm for an N × N image is O (2N 2 log N). When compared with the BDND method, EBDND method has two advantages given as follows.
- An efficient-sorting method is used both in the noise detection and adaptation stages, achieving a time complexity of O (2N ), which reduces computational time drastically.
- In filter scheme, EBDND method does not need to estimate noise density level and maximum window size for the EBDND method is 5.
| 6. Experimental Results | | |
The performance of the proposed EBDND method is compared with that of the BDND method by visual quality of the restored video sequences and runtime consumed. The current TV sets operate in the (Luma and Chrominance) YUV domain or in the Red, Green and Blue (RGB) Domain, but the hardware complexity can be reduced if YUV domain processing is chosen due to the lower amount of data in chrominance channel. Definition of the digital signals Y, U, V, from the primary signals R,G and B is follows [21] :
Y = 0.299R + 0.587G + 0.114B
U = 0.492 (B-Y)
V = 0.877 (R-Y)
In our simulation experiments, "news" and "waterfall" color video sequences in the YUV domain are taken and converted to grayscale (each frame of 352 × 288 width × height). These sequences contain 300 frames each. Frame 1 (considered as image) of the two video sequences (news and waterfall) are shown in [Figure 2]. The frames contaminated by salt-and-pepper noise with 70% noise density are shown in [Figure 3]. The restoration results for the first frame of two sequences using EBDND and BDND method are shown in [Figure 4] and [Figure 5], respectively. In [Figure 4] and [Figure 5], it is seen that the video quality of the EBDND method is the same as that of BDND method. For restoration of the consecutive frames (here frames 10 and 50 of waterfall sequence and frames 20 and 181 of news sequence), the motion compensated median filter is applied on the displaced previous frame elements. | Figure 3: Frame 1 of "news" and "waterfall" sequence corrupted by 70% noise density.
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 | Figure 4: Frame 1 of "news" and "waterfall" sequence restored using proposed EBDND method.
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 | Figure 5: Frame 1 of "news" and "waterfall" sequence restored using BDND method.
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The original frames 20 and 181 of "news" sequence along with frames corrupted by 70% noise density, restored frames using EBDND and BDND methods with fast motion compensation algorithm are shown in [Figure 6],[Figure 7],[Figure 8] and [Figure 9], respectively. Similarly, those for the "waterfall" sequence of original frames 10 and 50 and the ones corrupted with 70% noise density are shown in [Figure 10],[Figure 11],[Figure 12] and [Figure 13], respectively. | Figure 7: Frames 20 and 181 of "news" sequence corrupted by 70% noise density.
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 | Figure 8: Frames 20 and 181 of "news" sequence restored using proposed EBDND method with motion compensation.
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 | Figure 9: Frames 20 and 181 of "news" sequence restored using BDND method with motion compensation.
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 | Figure 11: Frames 10 and 50 of "waterfall" sequence corrupted by 70 % noise density.
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 | Figure 12: Frames 10 and 50 of "waterfall" sequence restored using proposed EBDND method with motion compensation.
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 | Figure 13: Frames 10 and 50 of "waterfall" sequence restored using BDND method with motion compensation.
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Simulations are carried out under a wide range of noise density levels (from 10 to 90%). The runtime analysis of the EBDND and BDND methods are conducted for "news" and "waterfall" video sequences using INTEL 2.8GHz processor with 512 MB RAM.
[Table 1] illustrates the runtime results of the EBDND with BDND method. The runtime results of the successive frames using motion compensated median filtering are shown in [Table 2] and [Table 3], respectively. Results reveal that EBDND method is much faster than BDND method. For two different video sequences, EBDND method is taking almost same time [since worst case time complexity is O (2N )] for a given noise density, whereas BDND method is consuming more time for "waterfall" sequence than "news" sequence since "waterfall" sequence has varying pixels in the entire frame. It is also observed that, with the increase of noise density, processing takes more time for initial frame than for successive frames and the restoration of successive frames depend on previous frame results. | Table 1: Runtime results of the proposed EBDND and BDND methods on frame 1 of waterfall and news sequences
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 | Table 2: Runtime results (seconds) of the proposed EBDND and BDND methods on frame 50 of water fall and frame 181 of news sequences with motion compensation
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 | Table 3: Runtime results (seconds) of the proposed EBDND method and BDND method with motion compensation
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The proposed median filtering with motion compensation is applied on successive frames (10 and 20) of two sequences. This involves filtering only displaced previous frame elements, resulting in reduction of the processing time.
The PSNR of the EBDND and BDND methods are computed using the following formula:
Where I is original image pixel, K is the recovered image pixel; MSE is the mean squared error.
[Table 4] summarizes PSNR measurement of the EBDND and BDND method incorporated on test image (frame 1 of "news" and "waterfall" sequence) being corrupted by a noise density of 70%, but comprising different densities of "salt" and "pepper" noise. | Table 4: PSNR comparison of the proposed EBDND and BDND methods for a noise density of 70%
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[Table 5] and [Table 6] summarize PSNR measurements of the EBDND and BDND method incorporated on test frames (20 and 181 of "news", 10 and 50 of "waterfall" sequence) being corrupted by different noise densities from 10 to 90%. | Table 5: Noise density vs PSNR comparison of the proposed EBDND and BDND methods for frame 10 of waterfall sequence and frame 20 of news sequence
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 | Table 6: Noise density vs PSNR comparison of the proposed EBDND and BDND methods for frame 50 of waterfall sequence and frame 181 of news sequence
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The improvement in PSNR (PSNR of the EBDND method-PSNR of the BDND method) is shown in [Figure 13] under various noise density levels for two video sequences. In [Figure 14] it is observed that the improvement in PSNR for the EBDND method increases with increase in noise density level.
[Table 5] and [Table 6] summarize PSNR measurement of the EBDND and BDND methods for different noise densities.
| 7. Conclusions | | |
In this paper, a fast and reliable motion compensated median filter with EBDND is proposed to remove impulse noise from images and video sequences especially at high noise level even with a noise density of 90%. The EBDND method is robust as compared with the BDND method. Experimental results show that it is faster than BDND requiring less computation time. Further, the restoration video sequence results have shown that the video quality of the EBDND method is same as that of BDND.
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| Authors | | |
 T. Ravi Kishore received the B.Tech degree from JNT University, AP, India in Electronics and Communication Engineering, and the Masters degree in signal processing from Osmania University, Hyderabad, India in 2005. He joined Defence electronics research Laboratory (DLRL), DRDO, Hyderabad, India as Scientist, in 2005. He has been working in the area of signal processing for electronic warfare systems with specific interest in the area of modulation classification for radar signals. His research interests include image denoising, image retrievals, analysis and classifications of low probability of intercept (LPI) signals.
 K. Deergha Rao received his B.E. and M.E. degrees from Andhra University, Visakhapatnam, India, in 1977 and 1980 respectively, and Ph.D. degree in Electronics and Communication Engineering from Osmania University, Hyderabad, India, in 1993. He is a senior member of IEEE, and chairman of Communications and Signal Processing societies joint chapter of IEEE Hyderabad Section.
He is presently a professor in the Research and Training Unit for Navigational Electronics, Osmania University. He served as a postdoctoral fellow and part-time professor from March 1999 to March 2003 in the Dept. of ECE, Concordia University, Montreal, Canada. As part-time professor, he has taught the courses Digital Signal Processing and Channel coding to the Master and Ph.D students at, Concordia University.
He has presented papers at IEEE International conferences several times in USA, Switzerland, and Russia. His research interests include GPS signal processing, Wireless channel coding, Blind Equalization, Robust Multiuser detection, OFDM UWB signal processing, Image processing, Cryptosystems, VLSI signal processing. So far one Ph.D was awarded under his guidance and presently six students are working towards Ph.D under his guidance. He has more than 100 publications to his credit including 50 publications in IEEE journals and conference proceedings
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12], [Figure 13], [Figure 14]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6]
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