Article Contents
Article Contents

# 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[13] 14249 1928 16177 20596 3602 24198 31165 6668 37833 Luo[24] 14365 1713 16078 20596 2135 22371 33374 2886 36260 CEF[17] 14727 6141 20868 17490 7745 25235 21314 8657 29971 ASWM[2] 7381 11042 18423 10614 12050 22664 19577 16845 36422 DWM[15] 11600 7937 19537 15035 8652 23687 15373 14215 29588 ROR-NLM[32] 12443 3056 15499 15778 3655 19433 21601 5917 27518 ROAD[16] 13476 8079 21555 13771 10055 23826 17212 9330 26542 ROLD[14] 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[13] 29.58 24.63 20.40 23.52 21.41 19.12 27.09 25.47 23.41 Luo[24] 30.77 27.16 22.62 23.59 21.62 19.17 27.00 25.33 22.78 CEF[17] 32.11 29.76 25.90 23.85 22.79 21.41 27.16 26.24 25.12 ASWM[2] 32.29 29.23 25.04 23.97 22.58 21.11 27.29 26.20 24.98 DWM[15] 32.34 29.32 25.49 24.07 22.58 21.13 27.23 26.07 25.03 ROR-NLM[32] 32.97 30.02 25.60 24.18 22.84 21.19 27.68 26.56 25.36 ROAD[16] 32.07 30.24 27.42 23.73 23.09 21.88 26.61 25.92 24.82 ROLD[14] 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
•  E. Abreu , M. Lightstone  and  S. K. Mitra , A new efficient approach for the removal of impulse noise from highly corrupted images, IEEE Transactions on Image Processing, 5 (1996) , 1012-1025.  doi: 10.1109/83.503916. S. Akkoul , R. Lédée  and  R. Leconge , A new adaptive switching median filter, IEEE Signal Processing Letters, 17 (2010) , 587-590.  doi: 10.1109/LSP.2010.2048646. G. Arce  and  J. Paredes , Recursive weighted median filters admitting negative weights and their optimization, IEEE Transactions on Image Processing, 48 (2000) , 768-779.  doi: 10.1109/78.824671. A. S. Awad , Standard deviation for obtaining the optimal direction in the removal of impulse noise, IEEE Signal Processing Letters, 18 (2011) , 407-410.  doi: 10.1109/LSP.2011.2154330. M. J. Black  and  A. Rangarajan , On the unification of line processes, outlier rejection, and robust statistics with applications in early vision, International Journal of Computer Vision, 19 (1996) , 57-91.  doi: 10.1007/BF00131148. A. C. Bovik, Handbook of Image and Video Processing, 2nd edition, Academic press, 2010, New York, 2010. D. R. K. Brownrigg , The weighted median filter, Communications of the ACM, 27 (1984) , 807-818.  doi: 10.1145/358198.358222. J.-F. Cai , R. H. Chan  and  C. Fiore , Minimization of a detail-preserving regularization functional for impulse noise removal, IEEE Transactions on Image Processing, 29 (2007) , 79-91.  doi: 10.1007/s10851-007-0027-4. R. H. Chan , C.-W. Ho  and  M. Nikolova , Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization, IEEE Transactions on Image Processing, 14 (2005) , 1479-1485.  doi: 10.1109/TIP.2005.852196. R. H. Chan , C.-W. Ho  and  C.-Y. Leung , Minimization of detail-preserving regularization functional by Newton's method with continuation, Proceedings -International Conference on Image Processing, ICIP, 1 (2005) , 125-128.  doi: 10.1109/ICIP.2005.1529703. R. H. Chan , C. Hu  and  M. Nikolova , An iterative procedure for removing random-valued impulse noise, IEEE Signal Processing Letters, 11 (2004) , 921-924.  doi: 10.1109/LSP.2004.838190. P. Charbonnier , L. Blanc-Féraud  and  G. Aubert , Deterministic edge-preserving regularization in computed imaging, IEEE Transactions on Image Processing, 6 (1997) , 298-311.  doi: 10.1109/83.551699. T. Chen  and  H. R. Wu , Adaptive impulse detection using center-weighted medial filters, IEEE Transactions on Image Processing Letters, 8 (2001) , 1-3.  doi: 10.1109/97.889633. Y. Dong , H. R. Chan  and  S. Xu , Edge-preserving regularization, Image denoising, Noise detector, Random-valued impulse noise, IEEE Transactions on Image Processing, 16 (2007) , 1112-1120.  doi: 10.1109/TIP.2006.891348. Y. Dong  and  S. Xu , A new directional weighted median filter for removal of random-valued impulse noise, IEEE Transactions on Image Processing, 14 (2007) , 193-196.  doi: 10.1109/LSP.2006.884014. R. Garnett , T. Huegerich  and  C. Chui , A universal noise removal algorithm with an impulse detector, IEEE Transactions on Image Processing, 14 (2005) , 1747-1754.  doi: 10.1109/TIP.2005.857261. U. Ghaneka , A. K. Singh  and  and R. Pandey , A contrast enhancement-based filter for removal of random valued impulse noise, IEEE Signal Processing Letters, 17 (2010) , 47-50.  doi: 10.1109/LSP.2009.2032479. R. Gonzalez and R. Woods, Digital Image Processing, 2nd edition, Addision-Wesley Publishing Companyl, 2007. P. J. Green , Bayesian reconstructions from emission tomography data using a modified EM algorithm, IEEE Transactions on Medical Imaging, 9 (1990) , 84-93.  doi: 10.1109/42.52985. H. H. Dam , K. L. Teo  and  S. Nordebo , The dual parameterization approach to optimal least square FIR filter design subject to maximum error constraints, IEEE Transactions on Signal Processing, 48 (2000) , 2314-2320.  doi: 10.1109/78.852012. S. J. Ko  and  Y. H. Lee , Center weighted median filters and their applications to image enhancement, IEEE Transactions on Circuits and Systems, 38 (1991) , 984-993.  doi: 10.1109/31.83870. S. Z. Li , On discontinuity-adaptive smoothness priors in computer vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, 17 (1995) , 576-586.  doi: 10.1109/34.387504. L. Liu , C. P. Chen  and  Y. Zhou , A new weighted mean filter with a two-phase detector for removing impulse noise, Information Sciences, 315 (2015) , 1-16.  doi: 10.1016/j.ins.2015.03.067. W. Luo , A new efficient impulse detection algorithm for the removal of impulse noise, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 88 (2005) , 2579-2586.  doi: 10.1093/ietfec/e88-a.10.2579. M. Nikolova , A variational approach to remove outliers and impulse noise, Journal of Mathematical Imaging and Vision, 20 (2004) , 99-120.  doi: 10.1023/B:JMIV.0000011920.58935.9c. W. K. Pratt, Median Filtering, Image Proc Institute, University of Southern California, Los Angeles, Tech. Rep., 1975. F. Russo , Hybrid neuro-fuzzy filter for impulse noise removal, Pattern Recognition, 32 (1999) , 1843-1855.  doi: 10.1016/S0031-3203(99)00009-6. T. Sun  and  Y. Neuvo , Detail-preserving median based filters in image processing, Pattern Recognition Letters, 15 (1994) , 341-347.  doi: 10.1016/0167-8655(94)90082-5. K. Toh  and  N. Isa , Cluster-based adaptive fuzzy switching median filter for universal impulse noise reduction, IEEE Transactions on Consumer Electronics, 56 (2010) , 2560-2568.  doi: 10.1109/TCE.2010.5681141. D. Van De Ville , M. Nachtegael  and  D. Van der Weken , Noise reduction by fuzzy image filtering, IEEE Transactions on Fuzzy Systems, 11 (2003) , 429-436.  doi: 10.1109/TFUZZ.2003.814830. C. R. Vogel  and  M. E. Oman , Fast, robust total variation-based reconstruction of noisy, blurred images, IEEE Transactions on Image Processing, 7 (1998) , 813-824.  doi: 10.1109/83.679423. B. Xiong  and  Z. Yin , A universal denoising framework with a new impulse detector and nonlocal means, IEEE Transactions on Image Processing, 21 (2012) , 1663-1675.  doi: 10.1109/TIP.2011.2172804. H. Xu , G. Zhu  and  H. Peng , Adaptive fuzzy switching filter for images corrupted by impulse noise, Pattern Recognition Letters, 25 (2004) , 1657-1663.  doi: 10.1016/j.patrec.2004.05.025. M. E. Yüksel  and  A. Baştürk , A simple generalized neuro-fuzzy operator for efficient removal of impulse noise from highly corrupted digital images, AEU -International Journal of Electronics and Communications, 5 (1996) , 1012-1025.  doi: 10.1016/j.aeue.2004.10.002. M. E. Yüksel , A hybrid neuro-fuzzy filter for edge preserving restoration of images corrupted by impulse noise, IEEE Transactions on Image Processing, 15 (2006) , 928-936.  doi: 10.1109/TIP.2005.863941. X.-Y. Zeng  and  L.-H. Yang , Mixed impulse and gaussian noise removal using detail-preserving regularization, Optical Engineering, 49 (2010) , 097002-097002.  doi: 10.1117/1.3485756.

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