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发布时间: 2017-06-16 |
图像处理和编码 |
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郑渊悦, 徐铭恩, 王玲 |
收稿日期: 2016-12-14; 修回日期: 2017-03-01
基金项目: 国家高技术研究发展计划（863计划）（2015AA020303）；国家自然科学基金项目（KYZ193713071，KYZ193716041）
第一作者简介: 郑渊悦(1992-), 男, 杭州电子科技大学仪器科学与技术专业硕士研究生, 主要研究方向为医学图像处理。E-mail:im_zyy@hotmail.com
中图法分类号: TP391.9
文献标识码: A
文章编号: 1006-8961(2017)06-0778-09
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摘要
目的 超声图像斑点噪声会影响诊断的准确性和可靠性。通过分析超声图像斑点噪声统计模型，结合非局部均值滤波算法，提出一种基于超声斑点噪声模型的改进权值非局部均值（NLM）滤波算法。 方法 算法针对超声图像灰度信息对图像进行预处理，利用超声图像斑点噪声模型改进传统NLM算法的权值计算函数，基于图像特征确定最优采样间隔进行下采样，利用改进后的权值计算函数对图像进行NLM去噪处理。 结果 分别采用人工合成与真实超声图像对本文算法性能进行测试，并与传统非局部均值滤波算法、非局部总变分（NLTV）等算法进行去噪效果比较，同时采用均方误差、峰值信噪比和平均结构相似性作为滤波算法性能的客观评价指标。本文算法能快速完成超声图像的去噪处理，峰值信噪比较其他算法可以提高0.2 dB以上，可以降低均方误差，提高平均结构相似性，缩短处理时间，并得到较好的图像质量和视觉效果。 结论 根据超声图像斑点噪声模型对NLM算法的权值计算函数进行优化，使得NLM图像滤波算法能更好地适用于超声图像的去噪，基于超声斑点噪声模型的改进权值NLM算法相较于其他算法，滤波效果更佳，适合超声图像去噪。
关键词
图像去噪; 非局部均值; 斑点噪声; 超声图像; 下采样; 权重函数
Zheng Yuanyue, Xu Mingen, Wang Ling Abstract
Objective Medical ultrasound imaging, CT, MR, and X-ray imaging are four modern medical imaging techniques. Medical ultrasound imaging techniques are ultrasonic-based diagnostic imaging approaches used to visualize subcutaneous body structures, such as muscles, vessels, tendons, joints, and internal organs. Compared with other imaging techniques, medical ultrasound imaging is widely used in clinical diagnosis, especially in pregnant women and fetuses, because it is non-invasive, inexpensive, convenient, can be applied in real time, and so on. However, due to the influence of the ultrasonic imaging principle, the ultrasonic image is inevitably disturbed by speckle noise during the generation process, which not only reduces the quality of the ultrasonic image but also makes the identification and analysis of the image detail highly difficult. In this study, an improved non-local means (NLM) image denoising algorithm based on the noise model of the ultrasonic image is proposed. Method A statistical model of speckle noise is obtained based on the probability distribution of the ultrasonic image. Then, the Bayesian formula and speckle noise model are utilized to improve the weight function of the NLM filter algorithm. The weight function of the traditional NLM algorithm is based on Gaussian distribution, so it can suppress Gaussian noise well. However, it is unsuitable for speckle noise. In this study, the weight function is improved based on the speckle noise model to make the algorithm applicable to an ultrasonic image. The algorithm preprocesses the image according to the characteristics of the proposed weight function by using a pre-defined threshold. If the average gray value of the image is greater than 155, then the image is processed directly. If the average gray value of the image is less than 100, then the anti-colored image is used for denoising. If the image has an average gray value of 100 to 155, both the original and anti-colored images are processed, and the average of the results is calculated and used as the final result. This step makes the algorithm produce a good denoising effect. Afterward, different sampling intervals are utilized to subsample the image; each sampling interval must be smaller than the similar window size in the NLM algorithm. For each pixel in the sampled block, the filtered value is calculated with the improved NLM algorithm. If a pixel is in the intersection of two sampled blocks, the final estimated value of the pixel is calculated by the weighted average of the filtered values in the two sampled blocks. After all the pixels are calculated, de-speckling performances in terms of filtered time, peak signal-to-noise ratio (PSNR), mean squared error (MSE), and mean structural similarity (MSSIM) at different sampling intervals are analyzed to optimize the sampling interval so that the algorithm can reduce noise while reducing the processing time. Finally, the optimized sampling interval and the improved NLM algorithm are applied to ultrasonic image denoising. Result The search and image window sizes are fixed to 11×11 and 5×5, respectively, in the optimized Bayesian NLM algorithm (OBNLM) algorithm and the proposed algorithm. The optimal sampling interval is fixed to 3 according to the experimental results. Experiments on phantom images and real 2D ultrasound datasets show that the proposed algorithm outperforms other well-accepted methods, including the traditional NLM algorithm, OBNLM, non-local total variation (NLTV) algorithm, and speckle-reducing anisotropic diffusion filter (SRAD), in terms of objective and subjective evaluations (e.g., MSE, PSNR, MSSIM, and computational time). The images filtered with the proposed algorithm have a higher PSNR value than the other de-speckling algorithms, which means the proposed algorithm can preserve the details of the image information better, and the filtered image has similar edges as the noise-free image. Comparison of MSE and MSSIM values indicates that the proposed algorithm has lower MSE values and higher MSSIM values than the others, which means the proposed algorithm can better preserve the structure information of the original image. With regard to computation time, the proposed algorithm does not demonstrate superiority in this aspect, but the speed of the proposed algorithm is almost nine times faster than that of the traditional NLM algorithm. An experiment is also conducted on real 2D ultrasound images, and results show that the proposed algorithm provides a better visual effect than other well-accepted methods. Conclusion Speckle noise reduces the quality of ultrasonic images and limits the development of automatic diagnostic technology. According to the speckle noise model of ultrasonic images, the weight function of the NLM algorithm is optimized to make the algorithm suitable for ultrasonic image denoising. Experimental results show that the proposed algorithm is better than other algorithms and suitable for ultrasonic image denoising.
Key words
despeckle; non-local means; speckle noise; ultrasonic image; subsample; weight function
0 引言
与其他医学影像成像方式相比，超声成像具有无创、无损、廉价、方便、实时等优点，被广泛地运用于医学临床诊断中，尤其是孕妇胎儿成长状况的检查。然而，由于受超声自身成像原理的影响，超声图像在产生过程中不可避免地会受到斑点噪声的干扰[1]，使得采集的超声图像对比度有限。因此，抑制超声图像中的斑点噪声是对超声图像进行后续分析和处理的重要前提。
为提高超声图像质量，人们已经提出许多抑制图像斑点噪声的方法[2]。这些方法可简单分成5类：经典的自适应去噪方法，包括Lee滤波[3]，Frost滤波[4]，Kuan滤波[5]，自适应中值滤波[6](AWMF)等；基于小波变换[7-8]的多尺度去噪方法，如小波软/硬阈值法等；基于偏微分方程的各向异性扩散[9-11](AD)去噪方法和全变分(TV)最小模型[12]去噪方法等；非局部均值(NLM)去噪方法，包括传统NLM、OBNLM等。以及对前几种方法进行混合的去噪方法，如非局部总变分[13](NLTV)去噪方法、3维块匹配[14]去噪方法等。
非局部均值滤波[15-16]算法是近几年兴起的图像滤波算法，其基本思想是每幅图像都包含了许多冗余信息，每个像素点的像素值都与该图像中其他像素相关。当图像受噪声污染时，可以在整幅图像中寻找与该噪声点具有相似结构的区域，通过计算这些区域与当前噪声点所在图像块之间的相似程度作为权重来估计当前噪声点的像素值[17-18]。该算法对于高斯噪声有着很好的去噪效果，但是对超声图像的斑点噪声的去除效果并不理想。主要原因是非局部均值滤波算法计算图像块之间的相似程度使用的是高斯加权欧氏距离，这并不适用于超声图像非加性的斑点噪声。
针对传统NLM图像滤波算法对超声图像斑点噪声滤出效果不佳，提出了一种基于斑点噪声分布特征的改进NLM超声图像去噪算法。
1 NLM图像去噪算法
NLM图像去噪算法是计算整幅图像不同区域与目标点邻域的相似程度，通过加权平均得到目标点的估计值。相似程度的计算由像素点的灰度值以及其周围的邻域结构共同决定。NLM算法的具体过程如下：
已知1幅受噪声污染的图像
| $ NL(v)(x) = \sum\limits_{y \in \mathit{I}} {w\left( {x,y} \right)v\left( y \right)} $ | (1) |
式中，权重系数
| $ w(x,y) = \frac{1}{{C(x)}}{{\rm{e}}^{ - \frac{{\sum\limits_{{x_i} \in {N_x},{y_i} \in {N_y}} {\left\| {v({x_i}) - v({y_i})} \right\|_a^2} }}{{{h^2}}}}} $ | (2) |
| $ C(x) = \sum\limits_{x \in I} {{{\rm{e}}^{ - \frac{{\sum {\left\| {v(x) - v(y)} \right\|_a^2} }}{{{h^2}}}}}} $ | (3) |
式中，
2 超声图像噪声模型及改进算法
2.1 超声噪声模型
超声图像在产生的过程中会受电子元器件内部电子随机热运动产生的电子噪声、高频器件产生的电磁干扰噪声以及超声波在人体内组织表面散射并相互干涉产生的斑点噪声的干扰，其中前两种属于加性噪声，后一种属于乘性噪声，因此Jain于1989年提出了乘性与加性噪声组合的模型
| $ u(x) = v(x)*{n_m} + {n_a} $ | (4) |
式中，
| $ u(x) = v(x) + {v^\gamma }\left( x \right)\theta \left( x \right) $ | (5) |
式中，
2.2 欧氏距离的改进
文献[19]指出，NLM图像去噪算法可通过贝叶斯公式进行改写，即
| $ \hat u(x) = \frac{{\sum\limits_{y \in I} {p(v(x)\left| {v(y))} \right.p(v(y))v(y)} }}{{\sum\limits_{y \in I} {p(v(x)\left| {v(y))} \right.p(v(y))} }} $ | (6) |
式中，
若图像受均值为0，方差为
| $ NL(v)(x) = \frac{1}{Z}\sum\limits_{y \in I} {{e^{ - \frac{{\left\| {v(x) - v(y)} \right\|_a^2}}{{2{\sigma ^2}}}}}} v(y) $ | (7) |
若令
| $ NL(v)(x) = \frac{1}{Z}\sum\limits_{y \in I} {{e^{ - \frac{{\left\| {v(x) - v(y)} \right\|_a^2}}{{2v\left( y \right)2{\sigma ^2}}}}}} v(y) $ | (8) |
当图像的灰度值较大时，加权欧氏距离较大，对图像的平滑能力较强，可以更好地去除噪声，反之若图像的灰度值较小时，算法对图像的平滑程度较低，去噪效果不明显。因此，本文在对图像进行处理之前，先对图像的灰度值范围进行预先判断，根据图像不同的灰度情况作不同处理。若图像的平均灰度值大于155，则直接进行处理，若图像平均灰度值小于100，则先对图像反色，再用去噪算法进行处理，若图像平均灰度值介于两者之间，则分别进行两次处理取均值。采用此方法可以较大程度地滤除图像中的噪声，但可能会导致图像细节信息的丢失，因此本文通过限制权重计算公式，在去噪的同时保留图像的细节信息，即
| $ w(x,y) = \left\{ \begin{array}{l} \frac{1}{Z}{{\rm {e}}^{ - \frac{{\sum\limits_{{x_i} \in {N_x},{y_i} \in {N_y}} {\left\| {v({x_i}) - v({y_i})} \right\|_a^2} }}{{2v\left( {{y_i}} \right)2{\sigma ^2}}}}}\;\;\mu \le \frac{{\overline {v\left( x \right)} }}{{\overline {v\left( y \right)} }} < \frac{1}{\mu }\\ 0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm{其他}} \end{array} \right. $ | (9) |
2.3 下采样
NLM图像滤波算法对高斯噪声有很好的去噪效果，但是其计算的时间复杂度过高。如果处理一幅大小为
具体步骤如下：
1) 令
2) 对于每个图像块
| $ NL(v)(x) = \sum\limits_{y \in I} {{{\rm{e}}^{ - \frac{{\left\| {v({x_i}) - v({y_i})} \right\|_a^2}}{{2v\left( y \right)2{\sigma ^2}}}}}} v\left( y \right) $ | (10) |
| $ {Z_{x,{B_i}}} = \sum\limits_{y \in I} {{{\rm{e}}^{ - \frac{{\left\| {v({x_i}) - v({y_i})} \right\|_a^2}}{{2v\left( y \right)2{\sigma ^2}}}}}} $ | (11) |
式(10) 计算得到的是图像块
3) 如果一个像素点同时属于多个图像块，则将对应区块中的估计值和权值归一化系数进行求和，再进行归一化处理，得到最终的估计值。若像素点仅属于某一个图像块，则直接使用式(11) 求得的权值归一化系数进行归一化处理。
理论上通过下采样处理后，可以使算法计算的时间复杂度降为原先的
本算法的下采样步骤与OBNLM方法类似。OBNLM先计算相似窗中每个像素点的估计值，对于重叠部分的像素点通过求和取均值来得到最终的估计值，本算法在计算每个相似窗中的像素点时，同时保留其计算过程中的权重和估计值，再对重叠区域的像素点通过加权平均来得到最终的估计值。相比之下，本算法可以提高相似区域对最终像素点的影响程度，从而得到更好的去噪效果。
3 实验结果与分析
NLM图像去噪算法中搜索窗和相似窗的大小对去噪性能和去噪速度有较大影响，为减少实验的变量，本文查阅相关文献并进行实验，选取搜索窗大小为11×11，相似窗大小为5×5，预处理阶段的阈值常数为0.9。为了客观地对图像去噪效果进行评价，本文选取了算法滤波时间、峰值信噪比(PSNR)、均方误差(MSE)和平均结构相似性(MSSIM)对算法的性能指标进行评估。
3.1 下采样间隔$n$ 的分析
为了确定最优的采样间隔，对不同噪声强度下不同采样间隔的图像进行了实验，其中采样间隔取值为1~9，使用的模拟超声斑点噪声模型为
| $ u\left( x \right) = v\left( x \right) + \sqrt {v\left( x \right)} \theta \left( x \right)\;\;\theta \left( x \right) \in N\left( {0,{\sigma ^2}} \right),{\sigma ^2} = \left[ {1,2,3,4} \right] $ |
实验使用的是matlab软件自带的Shepp-Logan模型图像。从图 1中可以看出，在采样间隔较小时，算法可以很好地滤除图像平滑区域的噪声，但随着采样间隔的不断增大，尤其是当采样间隔大于4时，算法的去噪能力明显降低，因此需要选择一个合适的采样间隔，在保证去噪效果的同时降低滤波时间。
3.1.1 时间性能分析
图 2(a)展示了测试图像在不同噪声强度下，不同采样间隔与滤波时间的关系。可以看出，采样间隔从1增加到2，滤波时间减少了将近4倍；增加到3时，滤波时间减少了将近9倍，这与理论分析是相符的，即随着采样间隔的增大，算法的时间复杂度降低为原先的
3.1.2 滤波性能分析
滤波算法对测试图像处理后的PSNR、MSE和MSSIM信息结果图 2(b)—(d)所示，其中图 2(b)—(d)中采样间隔为0指示的是原始噪声图像的PSNR、MSE和MSSIM信息。从图 2中可以直观地看出，随着采样间隔的增大，图像的去噪效果逐渐降低(PSNR减小，MSE增加，MSSIM减小)，当采样间隔大于等于5时，处理后图像的PSNR和MSE信息与噪声图像类似，说明此时滤波算法几乎不再起作用。这与2.3节提到的
3.2 与其他算法对比
为了进一步验证本文算法的去噪效果，分别对仿真图像和真实超声图像进行处理，并将实验结果与其他几种经典的去噪算法进行对比分析。表 1为仿真图像在不同噪声强度下使用不同去噪算法的PSNR、MSE和MSSIM，图 3为对应仿真图像的去噪效果图。可以看出随着噪声强度的增加，各类去噪算法的性能对应有所降低，但相比之下，本文的算法依旧能保持较好的去噪性能。在噪声强度较低时，传统NLM算法有较好的去噪效果，随着噪声强度的增大，本文算法逐渐体现其去噪优势。这是因为当图像噪声强度较低时，NLM算法通过计算当前像素与所有其他像素点灰度的加权平均，可以有效地保留图像的细节信息；但是当噪声强度增大后，图像每个像素的灰度值受噪声影响变大，可能会偏离原先的灰度值，使用该方法在计算权重信息时，会把噪声也同时带入计算，而本文算法通过大小为3的采样间隔进行采样，可以一定程度上减小噪声产生的影响，因此可以得到相对较好的去噪效果。SRAD算法结合自适应滤波算法和各向异性扩散滤波算法思想，对同质区域有着较好的去噪效果，因此当噪声强度较低时，SRAD算法的平均结构相似性(MSSIM)一直保持较高的水平。当噪声强度增大后，同质区域受噪声污染加重，因此SRAD算法的结构保持能力也逐渐减弱。本文相较于OBNLM算法，在下采样部分进行了优化，提高了相似区域的像素点对待估计像素的影响权重，因此处理后图像的质量有所提升。图 4~图 5为真实的超声图像的去噪结果，测试使用的真实超声图像均来自Ultrasoundcases.info网站。图 4展示了不同算法对肝脏超声图像的去噪结果，从视觉角度看，本文算法可以在去除噪声的同时有效地保留图像的细节信息。图 5为本文算法对不同组织超声图像的去噪结果。
表 1
不同仿真图像比较不同算法的MSE、PSNR和MSSIM值
Table 1
MSE、PSNR and MSSIM of despeckled images with different methods
| 算法 | |||||||||||
| MSE | PSNR/dB | MSSIM | MSE | PSNR/dB | MSSIM | MSE | PSNR/dB | MSSIM | |||
| 噪声图像 | 176.842 4 | 25.654 9 | 0.416 38 | 394.976 1 | 22.165 1 | 0.366 77 | 660.605 2 | 19.931 4 | 0.336 23 | ||
| Lee | 86.178 8 | 28.776 8 | 0.695 08 | 218.268 8 | 24.740 9 | 0.422 67 | 434.574 2 | 21.750 2 | 0.358 10 | ||
| SRAD | 131.72 2 | 26.934 2 | 0.917 02 | 181.444 2 | 25.543 4 | 0.587 64 | 290.119 2 | 23.505 0 | 0.411 08 | ||
| NWMD | 81.388 3 | 29.025 2 | 0.499 42 | 162.912 6 | 26.011 3 | 0.433 14 | 257.701 1 | 24.019 6 | 0.405 19 | ||
| NLM | 39.937 9 | 32.116 9 | 0.788 26 | 131.785 1 | 26.932 1 | 0.476 41 | 215.879 1 | 24.788 7 | 0.416 18 | ||
| OBNLM | 48.691 4 | 31.256 3 | 0.706 61 | 113.880 6 | 27.566 3 | 0.494 92 | 184.340 7 | 25.474 6 | 0.445 90 | ||
| NLTV | 58.676 6 | 30.446 2 | 0.587 31 | 123.454 3 | 27.215 7 | 0.492 41 | 193.337 0 | 25.267 7 | 0.446 18 | ||
| 本文 | 43.181 7 | 31.777 8 | 0.779 72 | 106.037 1 | 27.876 2 | 0.516 88 | 175.061 0 | 25.698 9 | 0.459 99 | ||
| 注：加粗字体对应的数据为每组性能指标中的最优值。 | |||||||||||
4 结论
本文通过分析超声图像的噪声模型，提出一种改进权值计算的NLM图像去噪算法。选取人工合成与真实超声图像进行实验，并与当前主流的斑点噪声抑制算法进行对比分析，实验结果表明，本文算法可以在减少算法处理时间的同时，能得到较好的去噪效果。在与人工合成算法进行对比的试验中可以看出，本文的算法相较于传统NLM算法速度可以提高近9倍，峰值信噪比可以提高0.2 dB以上。该算法为超声图像斑点噪声的抑制提供了新的思路，有助于提高超声图像质量。本文算法在实验中选取了固定大小的相似窗和搜索窗，对于相似窗和搜索窗大小对算法时间复杂度和斑点噪声抑制效果的影响有待进一步研究。
参考文献
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