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: January 2016

Revised: September 2016

Early access: May 2017

Published: April 2018

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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.

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

Citation:

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

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Figure 2. Directions and hops

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

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Figure 4. Total error detection

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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.

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

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

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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) \} $

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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

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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

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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

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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

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