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

Hao Yang; Hang Qiu; Leiting Chen

doi:10.3934/jimo.2017062

Article Contents

2018, Volume 14, Issue 2: 597-611. Doi: 10.3934/jimo.2017062

This issue Previous Article LP approach to exponential stabilization of singular linear positive time-delay systems via memory state feedback Next Article D.C. programming approach for solving an applied ore-processing problem

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

1.
School of Computer Science, Chengdu University of Information Technology, No.24 Block 1, Xuefu Road, 610225, Chengdu, China
2.
School of Computer Science and Engineering, University of Electronic Science and Technology of China, No.2006, Xiyuan Ave, 611731, Chengdu, China

* Corresponding author: Leiting Chen
* Corresponding author: Leiting Chen

Received: December 31, 2015

Revised: August 31, 2016

Early access: May 2017

Published: March 2018

Abstract Full Text(HTML) Figure(7) / Table(5) Related Papers Cited by

Abstract

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.

Keywords:

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

Citation:

Full Text(HTML)

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

Download: Full-size image PowerPoint slide

Figure 2. Directions and hops

Download: Full-size image PowerPoint slide

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

Download: Full-size image PowerPoint slide

Figure 4. Total error detection

Download: Full-size image PowerPoint slide

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.

Download: Full-size image PowerPoint slide

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

Download: Full-size image PowerPoint slide

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

Download: Full-size image PowerPoint slide

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) \} $

| Show Table

DownLoad: CSV

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

Method	40%			50%			60%
Method	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

| Show Table

DownLoad: CSV

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

Method	"Lena" image			"Bridge" image			"Pentagon" image
Method	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

| Show Table

DownLoad: CSV

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

Noise Density	Run Time(s)
Noise Density	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

| Show Table

DownLoad: CSV

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

Image Scale	Run Time(s)
Image Scale	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

| Show Table

DownLoad: CSV

Related Papers

Cited by

References

	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, 2^nd 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, 2^nd 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.