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# An optimized direction statistics for detecting and removing random-valued impulse noise

• * Corresponding author: Leiting Chen
• In this paper, we propose a robust local image statistic based on optimized direction, by which we can distinguish image details and edges from impulse noise effectively. Therefore it can identify noisy pixels more accurately. Meanwhile, we combine it with the edge-preserving regularization to remove random-valued impulse noise in the cause of precise estimated value. Simulation results show that our method can preserve edges and details efficiently even at high noise levels.

Mathematics Subject Classification: Primary: 94A08; Secondary: 47A52.

 Citation: • • Figure 1.  two kinds of edge contained in neighbor, (a) vertical edge, (b) slope edge

Figure 2.  Directions and hops

Figure 3.  The mean PSNR values associated with different $\alpha$ values

Figure 4.  Total error detection

Figure 5.  Results obtained by different algorithms for restoring the test lena image corrupted by random-valued impulse noise with 40 % noise density. (a) Noisy image, (b) ACWM, (c) Luo's method, (d) ASWM, (e) DWM, (f) ROAD-Trilateral, (g) ROR-NLM, (h) ROLD-EPR, (i) Proposed Method.

Figure 6.  Run time of detection vs. removal noises with different density

Figure 7.  Run time of detection vs. removal noises with different scale image

Table 1.  sets along the $l^{th}$ direction and hop count $h$

 $S^{(1)}_{1}=\{ (-1,-1); (0, 0); (1, 1) \}$ $S^{(1)}_{2}=\{ (-2,-2); (-1,-1); (0, 0); (1, 1); (2, 2) \}$ $S^{(2)}_{1}=\{ (0,-1); (0, 0); (0, 1) \}$ $S^{(2)}_{2}=\{(0,-2); (0,-1); (0, 0); (0, 1); (0, 2)\}$ $S^{(3)}_{1}=\{ (1,-1); (0, 0); (-1, 1 \}$ $S^{(3)}_{2}=\{(2,-2); (1,-1); (0, 0); (-1, 1); (-2, 2)\}$ $S^{(4)}_{1}=\{ (-1, 0); (0, 0); (1, 0) \}$ $S^{(4)}_{2}=\{(-2, 0); (-1, 0); (0, 0); (1, 0); (2, 0) \}$

Table 2.  Comparison of noise detection results for image "Lena" with various ratios of random-valued impulse noise

 Method 40% 50% 60% Miss False-hit Total Miss False-hit Total Miss False-hit Total ACWM 14249 1928 16177 20596 3602 24198 31165 6668 37833 Luo 14365 1713 16078 20596 2135 22371 33374 2886 36260 CEF 14727 6141 20868 17490 7745 25235 21314 8657 29971 ASWM 7381 11042 18423 10614 12050 22664 19577 16845 36422 DWM 11600 7937 19537 15035 8652 23687 15373 14215 29588 ROR-NLM 12443 3056 15499 15778 3655 19433 21601 5917 27518 ROAD 13476 8079 21555 13771 10055 23826 17212 9330 26542 ROLD 13987 7471 21458 16331 7875 24206 17245 9223 26468 Proposed 10158 5234 15392 11302 6583 17885 15234 7623 22857

Table 3.  Comparison of restoration results in PSNR for images corrupted with random-valued impulse noise

 Method "Lena" image "Bridge" image "Pentagon" image 40 % 50 % 60 % 40 % 50 % 60 % 40 % 50 % 60 % ACWM 29.58 24.63 20.40 23.52 21.41 19.12 27.09 25.47 23.41 Luo 30.77 27.16 22.62 23.59 21.62 19.17 27.00 25.33 22.78 CEF 32.11 29.76 25.90 23.85 22.79 21.41 27.16 26.24 25.12 ASWM 32.29 29.23 25.04 23.97 22.58 21.11 27.29 26.20 24.98 DWM 32.34 29.32 25.49 24.07 22.58 21.13 27.23 26.07 25.03 ROR-NLM 32.97 30.02 25.60 24.18 22.84 21.19 27.68 26.56 25.36 ROAD 32.07 30.24 27.42 23.73 23.09 21.88 26.61 25.92 24.82 ROLD 32.75 31.12 28.98 24.51 23.51 22.52 27.58 26.65 25.61 Proposed 33.62 31.73 29.56 24.98 23.82 22.79 27.92 26.98 25.93

Table 4.  Run time of detection vs. removal noises with different density

 Noise Density Run Time(s) Detection Removal Total 30 % 4.72 34.69 39.41 40 % 4.83 73.30 78.13 50 % 4.67 163.53 168.20 60 % 4.65 239.58 244.23 70 % 4.87 271.64 276.51

Table 5.  Run time of detection vs. removal noises with different scale image

 Image Scale Run Time(s) Detection Removal 64×64 0.38 5.5 128× 128 1.13 14.28 256×256 4.27 34.69 512×512 17.19 111.64
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