3. Image Impulse Noise Removal
3.5. Experiment Result
3.5.1. Simulation Results of Salt-Pepper Noise Removal
The performance of the proposed method has been examined on a variety of testing images corrupted with various noise densities. For quantitative performance evaluation, the peak signal-to-noise ratio (PSNR) defined as:
) ˆ )
( ( 255 log 10
1
2 2
10
∑
= −= N ×
n
n
n z
z
PSNR N (3.7)
is used as quantitative performance indication, where z is the gray level of original pixel; zˆ is the gray level of the final processed pixel and N is the total number of pixels in an image.
In our experiments, the proposed algorithm is compared with five existing methods including median filter [1], recursive median filter [2], Center Weighted Median (CWM) Filter [3], Tri-State Median Filter [14], and Li’s [24] method. Table 3.1 shows the quantitative comparisons of these different methods. It can be found that the proposed method can achieve best PSNR performance compared with the other methods.
The testing results of Lena with 20% impulse noise are shown in Fig. 3.10.
According to Fig. 3.10(c) and (d), we can find the recursive median filter removes the noise well but also blurs the edge, so the recursive algorithm cannot balance the noise removal and edge sharpness well. In Fig. 3.10(e) and (f), the Tri-State Median can retain more edge sharpness than the CWM, but both of them cannot remove the noise very well in some highly noise-corrupted area. In Fig. 3.10(g), Li’s method might misjudge some noisy pixels as the edge and then increase the size of some noises. The
threshold adjustment for different images is another problem that needs to be solved in these methods. In Fig. 3.11, the peppers images with 40% highly corrupted impulse noise are processed. It shows that the proposed method can effectively remove the noise and keep the edge sharpness well even in highly noise-corrupted conditions. Fig.
3.12 is the experimental results of the Boat image with 30% salt-pepper noise obtain from a public data base [63] to demonstrate the performance of the proposed method.
The reason why the proposed first-stage processing is so powerful in removing the impulse noise is that we take the advantage of adaptive-length median filter well especially for the images with high-density noise. In a high noise density region, the
5
5× median filter is applied to exhibit a high degree of noise suppression ability.
Otherwise, the noisy pixel is processed by the 3×3 median filter to preserve the sharpness. When images are highly corrupted by the noise, a large number of noisy pixels may connect into noise blotches and they cannot be removed well just by the processing of 3×3 median filter. In addition, the recursive and noise-exclusive scheme that allows only uncorrupted pixels inside the window to participate in median processing are also involved in the first stage to improve the performance of noise removal. According to the experimental results, it can be found that the one stage median type filtering wants to preserve the sharpness of the edges but leads to remain more un-removed noise pixels.
Fig. 3.13 and Table 3.2 show the essential importance of the image quality enhancement stage to compensate the blur and jaggy edge caused by the median filter and recursive algorithm. As the images are more highly corrupted, the large window size median filter (such as 5×5) is used more often to totally remove the noises. The image quality is further improved both in visual perception and quantity of PSNR after quality enhancement in the second step. Noise detection accuracy of the proposed method is shown in Table 3.3. Three detection measures are defined as
follows: “Total Correct Classification” [64] means the noisy pixels and uncorrupted pixels are correctly identified. “Un-detection” [22] means noise pixels are not identified that leads to residual noise. “Mis-detection” [22] means clean pixels are misidentified such that unnecessary filtering operation causes image blurring. Noisy pixels will be completely detected but few original pixels within the noise range will also be misidentified as noisy pixels. The median filtering result of the misdetected pixel is close to its original value and will not destroy the image quality too much.
The stable performances of experiment results verify our inference well.
Fig. 3.14 shows the experimental result of applying the proposed method to white noise that only maximum noisy pixels are found. The experiment result shows that the proposed method can also deal with the case that only maximum or minimum noisy pixels are existed pretty well.
Fig. 3.15 shows the performance comparisons of different noise removal methods with/without the proposed noise range assumption applying to “Lena”
corrupted with 40% impulse noise. Owing to only the detected noise pixels are filtered, they may prevent the blurring caused by filtering the uncorrupted pixels but still can’t remove the noise well. When images are highly corrupted, the noisy pixels may connect into noise blotches and they cannot be removed just by the processing of
3
3× median filter.
We also used the direct matrix inversion method to obtain the weighting matrices for the second-step processing. According to Fig. 3.16, we can find the second step processing that uses the weighting matrices obtained by matrix-based estimation method can also improve the compensation performance compared with the results of applying 1st step processing only. However, the neural network method still achieves better performance due to the variations of the training images and the selected training portions. The edge regions in the training images are separated into 8
different quantized angles. The variations may be caused by the quantization error (11.25o) and the characteristics of different images and regions. In addition, using nonlinearly filtered (median filters) results of the first stage (noise removal) to estimate the original clean pixels will also cause the variation and nonlinearity in the training.
The hardware and software environment that we implement the algorithms for speed comparisons are described as follows: all the algorithms are implemented in Matlab Language on a 1.8G Hz Pentium Ⅳ-based PC with 256 Mb RAM. Table 3.4 shows the average computation time in second for various algorithms applied to different kinds of noise corrupted images. The time consuming of the proposed algorithm is quite reasonable compared with other methods.
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Fig. 3.10. (a) Original image; (b) Lena with 20% of impulse noise; (c) the 3×3 standard median filter; (d) the 3×3 recursive standard median filter; (e) the recursive CWM filter with weight = 3; (f) the recursive Tri-state median filter with threshold = 25; (g) Li’s method with threshold = 32; (h) our proposed method.
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Fig. 3.11. (a) Original image; (b) Peppers with 40% of impulse noise; (c) the 3×3 standard median filter; (d) the 3×3 recursive standard median filter; (e) the recursive CWM filter with weight = 3; (f) the recursive Tri-state median filter with threshold = 25; (g) Li’s method with threshold = 32; (h) our proposed method.
(a) (b)
(c) (d)
(e) (f)
Fig. 3.12. (a) 30% Impulse Salt-Pepper noise [63]; (b) the 3×3 standard median filter; (c) the recursive Tri-state median filter with threshold = 25; (d) Li’s method with threshold = 32; (e) DMMD Denoise Software [65]; (f) our proposed method.
(a) (b)
(c) (d)
Fig. 3.13. (a) Original image; (b) Lena with 40% of impulse noise; (c) image after processing of the 1st step (impulse noise removal); (d) image after the processing of 2nd step ( image quality enhancement).
(a) (b)
Fig. 3.14. (a) Lena with 20% of white impulse noise; (b) processed by our proposed method.
(a) (b) (c)
(d) (e) (f)
Fig. 3.15. The performance comparisons of different noise removal methods with/without the proposed noise range assumption applying to “Lena” corrupted with 40% impulse noise. (a) and (d) the 3×3 recursive standard median filter with and without the noise range assumption, respectively. (b) and (e) the recursive Tri-state median filter (threshold = 25) with and without the noise range assumption, respectively. (c) and (f) Li’s method (threshold = 32) with and without the noise range assumption, respectively.
(a) (b) (c)
Fig. 3.16. Performance comparison of the matrix-based estimation method and the proposed neural network for the 2nd step compensation with respect to the Lena image with 40% of impulse noise. (a) Image after the processing of the 1st stage; (b) and (c) images after the 2nd step compensation by using the resultant weighting matrices of the matrix-based estimation and the proposed neural network, respectively.
Table 3.1 Quantitative comparisons of different noise removal methods applied to the images with various percentages of impulse noise.
(a)
Images Corrupted with 10 % Impulse Noise Filters
Lena Peppers Sailboat Baboon Aerial Boat Median 33.75 32.61 29.46 23.15 27.28 30.94 R-Median 32.55 32.24 28.40 22.66 25.75 29.72
CWM 3 [5] 34.45 33.36 30.72 25.13 28.49 31.97
Tri-State [14] 37.88 35.59 33.15 25.17 29.38 34.36
Li [24] 34.44 36.19 32.97 24.96 29.31 34.76
After our 1st step
processing 43.12 41.70 38.46 31.70 33.04 40.24
The complete processing of
our method 43.08 41.52 38.18 31.99 33.07 40.97
(b)
Images Corrupted with 20 % Impulse Noise Filters
Lena Peppers Sailboat Baboon Aerial Boat Median 29.65 28.78 26.94 22.09 25.14 27.88 R-Median 31.02 30.55 26.89 22.11 24.61 28.50
CWM 3 [5] 30.28 29.31 27.40 23.32 25.72 28.27
Tri-State [14] 31.76 30.33 28.70 23.64 26.47 29.49
Li [24] 32.70 30.90 29.52 23.73 27.06 30.91
After our 1st step
processing 39.40 37.72 34.70 28.60 30.98 36.45
The complete processing of
our method 39.74 38.18 34.61 28.86 31.19 37.31
(c)
Images Corrupted with 40 % Impulse Noise Filters
Lena Peppers Sailboat Baboon Aerial Boat Median 19.13 18.70 18.28 17.31 17.79 18.67 R-Median 26.86 25.79 23.45 20.69 22.01 24.84
CWM 3 [5] 20.18 19.54 19.02 18.30 18.64 19.56
Tri-State [14] 20.26 19.55 19.13 18.43 18.74 19.65
Li [24] 22.02 21.47 20.73 19.12 19.94 21.22
After our 1st step
processing 34.55 32.80 30.10 24.96 27.57 31.71
The complete processing of
our method 35.66 33.69 30.55 25.20 28.05 32.78
Table 3.2 Compensation ability of our adaptive median filter in the 1st step and the image quality enhancement system in the 2nd step with respect to Lena.
Impulse Noise Ratio 5 % 10 % 20 % 40 % Percentage of 5×5 Median filter
used in the 1st stage 0% 0.05% 0.31% 3%
PSNR after the processing of the 1st step 45.60 42.12 38.40 34.05 PSNR after the processing of the 2nd step 46.26 43.08 39.74 35.66 Total pixels of Mo>Th 8595 16525 33428 65651 Total pixels corrupted by the noise 13218 26007 52813 104868
Table 3.3 Noise detection accuracy of the proposed method with respect to “Lena”
image corrupted with various range and density of impulse noise.
Table 3.4 Speed Comparison for Various Algorithms (unit: sec)
Algorithm Median R-Median CWM 3 TRI Li’s The Proposed Ave. Time
(sec.) 52 54 53 100 700 120
Noise
Rate Noise Range Total Correct
Classification Un-detection Mis-detection
05 100.0 % 0.0 % 0.0 %
10 99.99 % 0.0 % 0.0007 %
20 99.998 % 0.0 % 0.002 %
10%
30 99.79% 0.0 % 0.21%
05 100.0 % 0.0 % 0.0 %
10 99.9993 % 0.0 % 0.0007 %
20 99.9977 % 0.0 % 0.0023 %
20%
30 99.815 % 0.0 % 0.185 %
05 100.0 % 0.0 % 0.0 %
10 99.9996 % 0.0 % 0.0004 %
20 99.9989 % 0.0 % 0.0011 %
40%
30 99.86 % 0.0 % 0.14 %