结合非下采样剪切波变换的BM3D去除图像噪声方法研究

樊华; 王文旭; 李晓阳; 陈睿; 韩贞辉

doi:10.11899/zzfy20230322

结合非下采样剪切波变换的BM3D去除图像噪声方法研究

doi: 10.11899/zzfy20230322

河南省地震局, 郑州 450018

基金项目: 中国地震局地震应急青年重点任务（CEA_EDEM-202111）；河南省青年人才托举工程项目（2022HYTP028）；中国地震局地震应急与信息青年重点任务（CEA_EDEM-202315）

详细信息

作者简介:
樊华，女，生于1988年。工程师。主要从事防震减灾公共服务、震害防御工作。E-mail：867877458@qq.com

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出版历程
- 收稿日期: 2022-07-26
- 刊出日期: 2023-08-31

BM3D Method Combined with Non-subsampled Shearlet Transform for Removing Image Noise

Henan Earthquake Agency, Zhengzhou 450018，China

摘要

摘要: 强噪声图像去噪一直是图像处理技术应用领域研究的热点，为进一步提高强噪声图像的去噪质量和对图像边缘的保护，针对三维块匹配（Block Matching 3D，BM3D）方法对强噪声图像去噪效果不佳及图像线状奇异性（如边缘）缺乏最优表示的问题，提出了基于二维非下采样剪切波变换（Non-subsampled Shearlet Transform，NSST）和BM3D的组合去噪方法。该方法首先对含噪图像进行NSST正变换，得到不同尺度和不同方向高频子带的剪切波系数；然后对每个尺度不同方向的高频子带求取贝叶斯阈值，并利用渐进半软阈值函数对各高频子带进行去噪；最后对低频子带和各去噪高频子带进行NSST逆变换，得到去噪结果。将去噪图像作为BM3D中基础估计阶段的预滤波，能够进一步提高基础估计阶段分组的正确性，为BM3D去噪奠定良好基础。组合去噪方法结合了NSST与BM3D的各自优势，仿真试验结果表明，对于低噪声图像，本方法和BM3D方法去噪效果相同，略优于非局部平均法；对于强噪声卫星影像，本方法去噪效果优于BM3D和非局部平均法。
- NSST /
- BM3D /
- 贝叶斯阈值 /
- 线状奇异性 /
- 渐进半软阈值函数
Abstract: Image denoising with strong noise (noise standard deviation σ≥40) is always a hot topic in the application field of image processing technology. In order to further improve the denoising quality and edge protection of images with strong noise, a combined denoising method based on 2D non-subsampled shearlet transform and BM3D was proposed to solve the problems of poor denoising effect of block-matching 3D (BM3D) on strong noise images and the lack of optimal representation of linear singularity (such as edge). Shearlet transform provides a local, multi-scale and multi-direction analysis method that can optimally represent the linear singularity of image. BM3D method has the best effect on image noise reduction (σ<40) among traditional noise reduction methods. The denoising steps of the combined method are as follows: Firstly, NSST forward transform is performed on the image with noise, and the shear wave coefficients of high-frequency subbands with different scales and directions are obtained. Then the Bayesian threshold values of the high-frequency subbands in different directions of each scale are obtained and the asymptotic semi-soft threshold function is used to denoise the high-frequency subbands. Finally, NSST inverse transform is performed on the low frequency subband and all the denoised high frequency subbands to obtain the denoising results. The denoised image is used as the pre-filter in the basic estimation stage of BM3D, which can further improve the correctness of the grouping in the basic estimation stage and lay a good foundation for the denoising of BM3D. The method of this paper combined the advantages of NSST and BM3D. Simulation results show that for low noise images, the method has the same denoising effect as BM3D, slightly better than that of NLmeans method. The method is superior to BM3D and NLmeans method for the denoising effect of satellite images with strong noise.
- NSST /
- BM3D /
- Bayesian threshold /
- Linear singularity /
- Asymptotically semi-soft threshold function

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图 1 频域自适应锥形划分

Figure 1. Adaptive tapered subgraph in frequency domain

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图 2 NSST三级分解示意

Figure 2. Schematic diagram of tertiary decomposition of NSST

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图 3 NSST去噪步骤示意

Figure 3. NSST denoising procedure diagram

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图 4 ST-BM3D算法流程

Figure 4. BM3D denoising process combined with NSST transform

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图 5 低噪声图像去噪效果对比

Figure 5. Contrast of weak noise images denoising effect

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图 6 强噪声图像去噪效果对比

Figure 6. Contrast of strong noise images denoising effect

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图 7 强噪声无人机图像去噪效果对比

Figure 7. Comparison of strong noise UAV image denoising

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图 8 强噪声卫星影像去噪效果对比

Figure 8. Comparison of strong noise satellite image denoising

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表 1 去噪方法性能评价结果

Table 1. Performance evaluation table of denoising method

图像名称	Lena图像		点线面高对比度图像		无人机图像		卫星影像
噪声值	（低高斯噪声标准差30 dB）		（强高斯噪声标准差100 dB）		（强高斯噪声标准差100 dB）		（强高斯噪声标准差100 dB）
评价参数	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
NL means方法	25.31	0.97	19.05	0.27	16.33	0.42	15.78	0.59
BM3D方法	28.56	0.98	23.94	0.43	22.07	0.60	21.32	0.74
本方法	28.61	0.98	26.05	0.75	23.03	0.71	22.42	0.80

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