基于三维剪切波变换和BM4D的图像去噪方法

doi:10.6040/j.issn.1672-3961.0.2019.262

摘要/Abstract

摘要：

针对传统的块匹配去噪方法只能处理二维图像的缺点，提出一种基于三维剪切波变换和改进的三维块匹配过滤(block-matching and 4D filtering, BM4D)算法的图像去噪方法。利用三维剪切波变换得到变换域系数，通过硬阈值和维纳滤波，在变换域中实现联合过滤。经过多尺度分解和方向剖分两个滤波阶段，确保三维剪切波变换是局部的；进行硬阈值和维纳滤波，分别包括分组、协同过滤和聚合3个步骤，利用堆积成四维组的体素立方体，在该组的四维变换同时利用每个立方体中体素之间存在的局部相关性和不同立方体中相应体素之间的非局部相关性。通过三维剪切波逆变换，得到每个分组立方体的估计值，在它们的原始位置进行自适应聚合。以峰值信噪比和结构相似度作为评价标准，试验结果表明：该方法不仅能够有效去除高噪声环境下的图像噪声，而且还能够有效地改善图像的视觉效果，具有较高的准确性。

关键词: 三维剪切波变换, 联合过滤, 协同过滤, 非局部相关性, 自适应聚合

Abstract:

Aimed at the disadvantage that the traditional block matching denoising method could only deal with two-dimensional images, an image denoising method based on 3D shearlet transform and BM4D(block-matching and 4D filtering) was proposed. This method used 3D shearlet transform to obtain transform domain coefficients, and realized joint filtering in transform domain through hard threshold and Wiener filtering stage. The 3D shearlet transformation was localized through two filtering stages: multi-scale decomposition and directional decomposition. The hard threshold and Wiener filtering were performed, which include grouping, collaborative filtering and aggregation. The 4D transformation of the cubes was based on the local correlationandon-local correlation cubes. The estimated values of each grouped cube were obtained by inverse transformation of 3D shearlet transform, and self-adaptive aggregation was performed at their original positions. PSNR(peak signal to noise ratio) and SSIM(structural similarity) were used as evaluation criteria. The results showed that this method could effectively remove image noise in high noise environment, and effectively improved the visual effect of the image with high accuracy.

Key words: 3D shearlet transform, combined filtering, collaborative filtering, non-local correlation, self-adaptive aggregation

中图分类号:

TP391.4

张胜男,王雷,常春红,郝本利. 基于三维剪切波变换和BM4D的图像去噪方法[J]. 山东大学学报 (工学版), 2020, 50(2): 83-90.

Shengnan ZHANG,Lei WANG,Chunhong CHANG,Benli HAO. Image denoising based on 3D shearlet transform and BM4D[J]. Journal of Shandong University(Engineering Science), 2020, 50(2): 83-90.

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去噪方法	评价指标	σ/%
去噪方法	评价指标	1	3	5	7	9	11	13	15	17	19
噪声数据	PSNR	40.00	30.46	26.02	23.10	20.91	19.17	17.72	16.48	15.39	14.42
噪声数据	SSIM	0.97	0.81	0.66	0.53	0.43	0.36	0.30	0.25	0.22	0.19
OB-NLM3D	PSNR	42.47	37.57	34.73	32.82	31.42	30.32	29.40	28.61	27.91	27.28
OB-NLM3D	SSIM	0.99	0.97	0.95	0.92	0.90	0.87	0.84	0.82	0.79	0.77
OB-NLM3D-WM	PSNR	42.52	37.75	35.01	33.13	31.73	30.61	29.68	28.88	28.18	27.55
OB-NLM3D-WM	SSIM	0.99	0.97	0.95	0.93	0.90	0.88	0.85	0.83	0.80	0.78
ODCT3D	PSNR	43.78	37.53	34.89	33.18	31.91	30.90	30.07	29.35	28.73	28.18
ODCT3D	SSIM	0.99	0.97	0.95	0.93	0.91	0.89	0.88	0.86	0.85	0.83
PRI-NLM3D	PSNR	44.04	38.26	35.51	33.67	32.37	31.29	30.40	29.65	28.99	28.40
PRI-NLM3D	SSIM	0.99	0.98	0.96	0.94	0.92	0.90	0.89	0.87	0.85	0.84
BM4D	PSNR	44.09	38.39	35.95	34.38	33.21	32.28	31.50	30.82	30.23	29.70
BM4D	SSIM	0.99	0.98	0.96	0.95	0.93	0.92	0.91	0.90	0.88	0.87
本研究	PSNR	45.00	39.19	36.62	34.94	33.70	32.70	31.88	31.19	30.58	30.05
本研究	SSIM	0.99	0.97	0.96	0.94	0.93	0.92	0.90	0.89	0.88	0.87

去噪方法	评价指标	σ/%
去噪方法	评价指标	1	3	5	7	9	11	13	15	17	19
噪声数据	PSNR	40.00	30.49	26.09	23.20	21.04	19.32	17.88	16.65	15.57	14.60
噪声数据	SSIM	0.97	0.81	0.66	0.53	0.43	0.36	0.30	0.25	0.21	0.18
OB-NLM3D	PSNR	42.41	37.45	34.54	32.51	30.97	29.71	28.62	27.64	26.74	25.91
OB-NLM3D	SSIM	0.99	0.97	0.94	0.91	0.88	0.85	0.81	0.78	0.74	0.70
OB-NLM3D-WM	PSNR	42.44	37.54	34.66	32.61	31.01	29.69	28.53	27.50	26.57	25.71
OB-NLM3D-WM	SSIM	0.99	0.97	0.95	0.92	0.88	0.85	0.81	0.77	0.74	0.70
ODCT3D	PSNR	42.96	37.38	34.70	32.90	31.53	30.41	29.48	28.67	27.95	27.30
ODCT3D	SSIM	0.99	0.97	0.95	0.93	0.90	0.88	0.86	0.84	0.82	0.80
PRI-NLM3D	PSNR	43.97	38.19	35.34	33.37	31.94	30.74	29.75	28.88	28.10	27.39
PRI-NLM3D	SSIM	0.99	0.98	0.96	0.94	0.91	0.89	0.87	0.85	0.82	0.80
BM4D	PSNR	44.08	38.34	35.83	34.17	32.89	31.82	30.90	30.06	29.29	28.57
BM4D	SSIM	0.99	0.98	0.96	0.94	0.93	0.91	0.89	0.88	0.86	0.84
本研究	PSNR	45.00	39.18	36.60	34.88	33.59	32.54	31.66	30.91	30.23	29.59
本研究	SSIM	0.99	0.97	0.96	0.94	0.93	0.91	0.90	0.89	0.87	0.85

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