基于最小错误率贝叶斯决策和平滑滤波的图像去噪算法研究
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摘要
图像信号在产生、传输过程中,经常会受到各种噪声的干扰,一般来说,现实中的图像通常都是带有噪声的。因此图像处理工作中,在进行图像分割、模式识别等高层次的处理前,选用适当方法尽可能的去除噪声的干扰是一个非常重要的预处理步骤。常用的图像去噪方法有:均值滤波和中值滤波以及由它们衍生出的各种改进型去噪算法。但是这些方法通常都是对图像的每一个像素点进行平滑,常将应保留的图像边缘及细节作了修改,从而造成图像信息的改变。近年来,小波分析得到了快速发展,在图像处理方面,小波图像去噪受到了国内外学者的重视,是当今热门的研究课题,因此陆续出现了一系列方法,如自适应软(硬)阈值去噪方法,模极大值去噪方法,最优模糊阈值去噪方法等算法在图像去噪处理中都取得了一定的效果。但应用小波去噪时,选取有效合理的小波基或小波基的参数比较困难,而且还存在争议。因此,如何有效的去除噪声且保持图像清晰度是本文研究的重点。
本论文首先简要介绍了图像去噪处理的意义、研究现状,然后对传统的图像去噪方法进行了介绍,接着分析了贝叶斯决策的基本理论及常用的贝叶斯决策方法,在此基础上,通过观察加噪图像及其直方图的变化,了解到去噪的前提是准确地检测噪声,而无论何种去噪方法都不可能完全准确的检测出每一个噪声点,基于此提出了检测噪声时使出错率尽可能小,且仅对检测出的噪声点进行平滑的算法。
本文应用最小错误率贝叶斯决策来检测噪声,并提出针对检测出的噪声采用不同的滤波方法,滤波时只应用判定为非噪声点的像素点对噪声点进行平滑。研究工作主要集中在以下几个方面:
1、引入最小错误率贝叶斯决策,用于检测噪声点,使检测噪声时的出错率尽可能小。针对应用最小错误率贝叶斯决策时原图像的类条件概率密度难以计算的情况,引入类条件概率密度的离散化计算,避免了常用的对类条件概率密度的估计假设,使其更符合类别的分布情况。
2、引入Otsu法并对其进行了简化和改进,应用简化和改进后的Otsu法进行噪声及目标的自动最优阈值选取。从而避免了将噪声灰度绝对化的可能及需要多次实验获取阈值的复杂过程。另外对椒盐噪声图中的黑白噪声阈值采用双向同时计算来获取两个阈值。
3、根据噪声种类的不同,对应用最小错误率贝叶斯决策检测出的噪声采用不同的平滑滤波方法,在滤波时预先对要参与滤波的像素点进行检测,仅利用检测为非噪声点的像素点对当前判定为噪声的像素点进行平滑,从而排除了采用噪声像素点进行滤波而带来二次污染的可能性。
4、对处理后图像质量进行了分析,提出以信噪比为评价条件对图像进行循环检测滤波,使多次处理后的图像信噪比最高,从而使处理后的图像质量尽可能的优化。实验结果表明,该算法的去噪效果大大优于其他一些方法,尤其对噪声密度较大的图像取得的效果更佳。
为了验证算法的有效性,本文采用VC++6.0编程环境分别对不同噪声类别、噪声强度的带噪图像进行滤波检测,并与传统去噪方法进行了效果比较。结果表明,本文提出的算法能有效去除噪声并在一定程度上保留了图像细节。
When the image signals are generated and transmitted, they are regularly interfered with by a variety of noise. In general, real images usually contain noise. Therefore, in image processing work, it is very important that we use appropriate methods to remove noise interference before carrying out image segmentation; pattern recognition. Average filtering and median filtering are commonly used to remove image noise. There is a usual way to remove noise that is, a variety of improved denoising algorithms derive from average filtering and median filtering. However, these methods usually smooth each pixel of image. So they will revise the image’s edges and details which should be retained in the image. As a result, the imformation of image is changed. In recent years, wavelet analysis has been rapidly developed. In image processing, wavelet image denoising has been paid more attention to by domestic and foreign scholars and has become hot topic. Then a series of methods appeared, such as adaptive soft (hard) threshold denoising method, modulus maxing denoising method, optimal fuzzy threshold denoising method. They have achieved some results. But it is difficult and controversial to select the effective and rational wavelet or wavelet parameters in the application of wavelet denoising. Therefore, the focus of this paper is how to effectively remove noise and preserve image clarity as much as possible.
Firstly, this paper briefly describes the significance of image denoising and the status quo. Then we give an introduction of the traditional image denoising methods. Next, we analyse the basic theory of Bayesian decision-making and general Bayesian decision-making methods. On this basis, we learn that the premise of denoising is accurate detection of noise through observating the image and its histogram. No matter which the denoising method we use, we can not accurately detect each noise point. So we can make error rate as small as possible when we detect denoising, and only smooth the noise point.
In this paper, we use the minimum error rate of Bayesian decision-making to detect noise. And different filtering methods are used to remove different type’s noises. At last we only use the point which is not noise point to filter. Research work focuses on the following aspects:
1. Introducing the minimum error rate Bayesian decision-making detects the noise. Then it will enable the error rate of detecting noise as small as possible. Because the calculation of the class conditional probability desity is difficult in the minimum error rate Bayesian decision-making, we use discrete method to compute it to avoid inaccurate estimates.
2. Introducing, simplifying and improving Otsu method computes threshold. We apply simplified and improved Otsu method to automaticly select the optimal threshold for noise and object. Thus it avoids the possibility of noise gray absolutization and the complex process of selecting threshold. In additon, we can also obtain two thresholds of salt and pepper noise image once.
3. Using different smoothing methods removes the different type’s noise. Regardless of using filtering method, the first step is to detect the participant pixel in order to prevent secondary pollution. Then only using non-noise points smooth the current point which is judged to be a noise. Thereby it precludes the possibility of secondary pollution which be produced due to using noise pixel to filter.
4. Anslysing the image quality after treatment implements loops detection filtering. The condition which judges image quality is Signal-to-Noise. So that we will get the highest signal to noise ratio and optimal image quality by loop processing. The experimental results show that the algorithm is much better than the de-noising effect of some other ways; especially for the high noise density of the image has a better effect.
In order to verify the effectiveness of the algorithm, this paper adopts VC++6.0 programming environment to test the image noise with different noise types, noise intensity respectively. The experimental results are compared with the traditional denoising method. The results show that the proposed algorithm can effectively remove the noise and retain image details to some extent.
本论文首先简要介绍了图像去噪处理的意义、研究现状,然后对传统的图像去噪方法进行了介绍,接着分析了贝叶斯决策的基本理论及常用的贝叶斯决策方法,在此基础上,通过观察加噪图像及其直方图的变化,了解到去噪的前提是准确地检测噪声,而无论何种去噪方法都不可能完全准确的检测出每一个噪声点,基于此提出了检测噪声时使出错率尽可能小,且仅对检测出的噪声点进行平滑的算法。
本文应用最小错误率贝叶斯决策来检测噪声,并提出针对检测出的噪声采用不同的滤波方法,滤波时只应用判定为非噪声点的像素点对噪声点进行平滑。研究工作主要集中在以下几个方面:
1、引入最小错误率贝叶斯决策,用于检测噪声点,使检测噪声时的出错率尽可能小。针对应用最小错误率贝叶斯决策时原图像的类条件概率密度难以计算的情况,引入类条件概率密度的离散化计算,避免了常用的对类条件概率密度的估计假设,使其更符合类别的分布情况。
2、引入Otsu法并对其进行了简化和改进,应用简化和改进后的Otsu法进行噪声及目标的自动最优阈值选取。从而避免了将噪声灰度绝对化的可能及需要多次实验获取阈值的复杂过程。另外对椒盐噪声图中的黑白噪声阈值采用双向同时计算来获取两个阈值。
3、根据噪声种类的不同,对应用最小错误率贝叶斯决策检测出的噪声采用不同的平滑滤波方法,在滤波时预先对要参与滤波的像素点进行检测,仅利用检测为非噪声点的像素点对当前判定为噪声的像素点进行平滑,从而排除了采用噪声像素点进行滤波而带来二次污染的可能性。
4、对处理后图像质量进行了分析,提出以信噪比为评价条件对图像进行循环检测滤波,使多次处理后的图像信噪比最高,从而使处理后的图像质量尽可能的优化。实验结果表明,该算法的去噪效果大大优于其他一些方法,尤其对噪声密度较大的图像取得的效果更佳。
为了验证算法的有效性,本文采用VC++6.0编程环境分别对不同噪声类别、噪声强度的带噪图像进行滤波检测,并与传统去噪方法进行了效果比较。结果表明,本文提出的算法能有效去除噪声并在一定程度上保留了图像细节。
When the image signals are generated and transmitted, they are regularly interfered with by a variety of noise. In general, real images usually contain noise. Therefore, in image processing work, it is very important that we use appropriate methods to remove noise interference before carrying out image segmentation; pattern recognition. Average filtering and median filtering are commonly used to remove image noise. There is a usual way to remove noise that is, a variety of improved denoising algorithms derive from average filtering and median filtering. However, these methods usually smooth each pixel of image. So they will revise the image’s edges and details which should be retained in the image. As a result, the imformation of image is changed. In recent years, wavelet analysis has been rapidly developed. In image processing, wavelet image denoising has been paid more attention to by domestic and foreign scholars and has become hot topic. Then a series of methods appeared, such as adaptive soft (hard) threshold denoising method, modulus maxing denoising method, optimal fuzzy threshold denoising method. They have achieved some results. But it is difficult and controversial to select the effective and rational wavelet or wavelet parameters in the application of wavelet denoising. Therefore, the focus of this paper is how to effectively remove noise and preserve image clarity as much as possible.
Firstly, this paper briefly describes the significance of image denoising and the status quo. Then we give an introduction of the traditional image denoising methods. Next, we analyse the basic theory of Bayesian decision-making and general Bayesian decision-making methods. On this basis, we learn that the premise of denoising is accurate detection of noise through observating the image and its histogram. No matter which the denoising method we use, we can not accurately detect each noise point. So we can make error rate as small as possible when we detect denoising, and only smooth the noise point.
In this paper, we use the minimum error rate of Bayesian decision-making to detect noise. And different filtering methods are used to remove different type’s noises. At last we only use the point which is not noise point to filter. Research work focuses on the following aspects:
1. Introducing the minimum error rate Bayesian decision-making detects the noise. Then it will enable the error rate of detecting noise as small as possible. Because the calculation of the class conditional probability desity is difficult in the minimum error rate Bayesian decision-making, we use discrete method to compute it to avoid inaccurate estimates.
2. Introducing, simplifying and improving Otsu method computes threshold. We apply simplified and improved Otsu method to automaticly select the optimal threshold for noise and object. Thus it avoids the possibility of noise gray absolutization and the complex process of selecting threshold. In additon, we can also obtain two thresholds of salt and pepper noise image once.
3. Using different smoothing methods removes the different type’s noise. Regardless of using filtering method, the first step is to detect the participant pixel in order to prevent secondary pollution. Then only using non-noise points smooth the current point which is judged to be a noise. Thereby it precludes the possibility of secondary pollution which be produced due to using noise pixel to filter.
4. Anslysing the image quality after treatment implements loops detection filtering. The condition which judges image quality is Signal-to-Noise. So that we will get the highest signal to noise ratio and optimal image quality by loop processing. The experimental results show that the algorithm is much better than the de-noising effect of some other ways; especially for the high noise density of the image has a better effect.
In order to verify the effectiveness of the algorithm, this paper adopts VC++6.0 programming environment to test the image noise with different noise types, noise intensity respectively. The experimental results are compared with the traditional denoising method. The results show that the proposed algorithm can effectively remove the noise and retain image details to some extent.
引文
[1] [2009-10-30]http://photo.hb666.com/html/200712/8/20071208232752.shtml.
[2]倪永婧.基于纹理细节的图像去噪算法的研究[D].秦皇岛:燕山大学,2006:1.
[3]杨淑莹.VC++图像处理程序设计[M].北京:清华大学出版社,北方交通大学出版社, 2006.
[4]王益艳,王晅,傅博,陈伟伟,梁娟.基于小波变换的图像自适应阈值去噪算法[J].微计算机应用,2008(1):15-18.
[5] R.Lukac,B.Smolka, K.Martin, K.N.Plataniotis,A.N.Venetsanopoulos,Vector filtering for color imaging, IEEE Signal Processing Magazine,Special Issue on Color Image Processing 2005,22 (1):74–86.
[6]杨辉.基于中值滤波和小波变换的图像去噪研究[D].长沙:湖南师范大学,2008.
[7]王益艳.图像去噪算法研究[D].西安:陕西师范大学,2008.
[8] Mallat S, Zhong S.Characterizat ion of signal frommult iscale edge [J]. IEEE Tran s PAMI, 1992, 14 (7):710- 732.
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[2]倪永婧.基于纹理细节的图像去噪算法的研究[D].秦皇岛:燕山大学,2006:1.
[3]杨淑莹.VC++图像处理程序设计[M].北京:清华大学出版社,北方交通大学出版社, 2006.
[4]王益艳,王晅,傅博,陈伟伟,梁娟.基于小波变换的图像自适应阈值去噪算法[J].微计算机应用,2008(1):15-18.
[5] R.Lukac,B.Smolka, K.Martin, K.N.Plataniotis,A.N.Venetsanopoulos,Vector filtering for color imaging, IEEE Signal Processing Magazine,Special Issue on Color Image Processing 2005,22 (1):74–86.
[6]杨辉.基于中值滤波和小波变换的图像去噪研究[D].长沙:湖南师范大学,2008.
[7]王益艳.图像去噪算法研究[D].西安:陕西师范大学,2008.
[8] Mallat S, Zhong S.Characterizat ion of signal frommult iscale edge [J]. IEEE Tran s PAMI, 1992, 14 (7):710- 732.
[9]李旭超,朱善安.基于小波模极大值和Meyman-Pearson准则阈值的图像去噪[J].中图图象图形学报,2005,10(8):964-969.
[10]黎健生.基于数值统计滤波和偏微分方程的图像平滑去噪算法研究[D].汕头:汕头大学,2008.
[11] S.M. Mahbubur Rahman, M.d. Kamrul Hasan. Wavelet-domain iterative center weighted median filter for image denoising. Signal Processing 83 (2003):1001-1012.
[12]杨光.基于神经网络和小波变换的MRI图像去噪方法[D].上海:华东师范大学,2007.
[13] Jian Zhao, Zhengwen Cao, Mingquan Zhou. SAR image denoising based on wavelet-fractal analysis. Journal of Systems Engineering and Electronics, 2007(18): 45-48.
[14]朱大龙.基于结构相似性的图像质量评价方法的研究[D].合肥:安徽大学,2006.
[15]张旭.数字滤波技术在医学图像去噪处理中的应用研究[D].太原:中北大学,2005.
[16]刘祝华.图像去噪方法研究[D].南昌:江西师范大学,2005.
[17]林晓梅.空间域图像去噪方法[J].长春工业大学学报,2004, 25(1):29-31.
[18] Ko S J, Lee S J. Center Weighted Median Filters and Their Applications to ImageEnhancement [J]. IEEE Trans, Circuits Syst, 1991, 38 (9): 984-993.
[19] Hwang H, Haddad Ra. Adaptive median filters: new algorithms and results [J]. IEEE Transactions on Image Processing, 1995, 4(4): 499-502.
[20] Barner K E,Aysal T C. Polynomial weighted median filtering [J]. IEEE Transactions on Signal Processing,2006,54:636-650.
[21]侯建华.基于小波及其统计特性的图像去噪方法研究[D].武汉:华中科技大学,2007.
[22]王香菊.基于中值滤波和小波变换的图像去噪方法研究[D].西安:西安科技大学,2008.
[23] Koray S. Erer. Adaptive usage of the Butterworth digital filter[J].Journal of Biomechanics, 2007 (40):2934–2943.
[24] R.M.Haralick, S.R.Sternberg, X.Zhuang. Image analysis using mathematical morphology, IEEE Trans. Pattern Anal. Machine Intell. 1987,9 (4):532–550.
[25] [2010-01-08]http://baike.baidu.com/view/852283.htm?fr=ala0_1[EB/OL].
[26] Isabelle Bloch, Henri Maitre. Fuzzy Mathematical Morphologies.Pattern Recognition, 28:(9)1341-1387.
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