一种新的基于中值滤波的优化滤波算法
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摘要
随着计算机技术的发展,数字图像处理技术近年来得到了极大的重视和广泛的应用,涌现出许多新理论、新方法。在实际应用中,由于通信信道等因素,数字图像中的原始信号总是和噪声共存的。使用图像滤波算法滤除噪声一直以来都是图像处理领域研究的热点,也是仍未得到圆满解决的研究课题。
椒盐噪声是现实应用中最常遇到的噪声类型之一,可以使用图像滤波器滤除这种噪声。中值滤波算法是最常用的非线性滤波算法之一,由于它简单实用,在很多领域得到了广泛的应用。但是标准中值滤波算法存在一些自身固有的缺点,具有很大的局限性。首先标准中值滤波的滤波效果与采用滤波窗口的大小有关,滤波窗口太小,去噪效果不好,窗口太大,会造成图像模糊；其次它对所有的像素点进行统一处理,这样虽然滤除了噪声点,但是也改变了信号点,造成了噪声在邻域的传播。
本文针对标准中值滤波算法在滤除噪声中的不足,提出了一种新的优化中值(ISM)滤波算法。该算法使用一个新的椒盐噪声判断标准,首先对图像局部各个方向上的灰度值信息进行统计分析,然后利用计算结果判断该点是否为噪声点。实验结果表明,与标准中值滤波算法相比,该算法可以有效地滤除图像中的椒盐噪声,同时还能很好地保留图像的细节。
本文首先介绍了数字图像的基础知识。然后分析了标准中值滤波的实现原理和缺陷不足,并对近几年出现的各种具有代表性的优化中值滤波算法进行了介绍和比较。在此基础上,本文创新性地提出了一种新的优化滤波算法,并描述了其具体实现的方法和步骤,最后给出了相关的计算机仿真实验数据。实验结果表明,该算法与标准中值滤波算法相比,可以有效地检测出噪声点,有更高的信噪比,同时拥有较低的漏检率和误检率,滤波性能更优良。
Whth the development of computer technology, the technologies of image processing gained great interests and wide applications, many new theories and new processing methods were proposed in recent years. Because of communication channel and so on, the signal pixels are always with noise pixels together. Image filter algorithm is always study focus in the field of image processing and analysis, which is still unresolved well till now.
Salt and pepper noise is a kind of common noises which can be eliminated by image filtering algorithms. The standard median filter is one of the most popular nonlinear fiters. Because standard median filter is simple and effective, it was widely used in many domains, but it had a very clear deficiency. The filter effects are influenced by the length of template window. Small template will lead to bad effects and big template will lead to image blurring. On the other hand, all the pixels are replaced with the median value of their neighborhood. Although the noise pixels are replaced, the signal pixels are also replaced that lead to the uncorrect spread of noise.
This paper presents a new improved median-based filtering algorithm to improve standard median filter algorithm. This algorithm gives a new decision criterion. Firstly, this decision citerion calculates the correlation value with its neighbors. And then the value is worked as the measure that we determine whether this pixel is a noise pixel. The simulation experiment shows that this algorithm can protect image signal detail as much as possible when effectively eliminates salt and pepper noise.
Firstly, this paper introduces the basic knowledge of digital image. And then introduces the principle of the standard median filter method, analyzes its deficiency and compares the standard median filter with many other new improved median filters. This paper presents an innovative improved median algorithm, makes a detailed exposition of the implementation method and gives simulation experiment data. At last, the simulation experiment shows that ISM filter can detect noise pixel effectively, get higher SNR and lower omission rate and lower false drop rate. So the ISM algorithm has better filtering performance than standard median filter.
椒盐噪声是现实应用中最常遇到的噪声类型之一,可以使用图像滤波器滤除这种噪声。中值滤波算法是最常用的非线性滤波算法之一,由于它简单实用,在很多领域得到了广泛的应用。但是标准中值滤波算法存在一些自身固有的缺点,具有很大的局限性。首先标准中值滤波的滤波效果与采用滤波窗口的大小有关,滤波窗口太小,去噪效果不好,窗口太大,会造成图像模糊；其次它对所有的像素点进行统一处理,这样虽然滤除了噪声点,但是也改变了信号点,造成了噪声在邻域的传播。
本文针对标准中值滤波算法在滤除噪声中的不足,提出了一种新的优化中值(ISM)滤波算法。该算法使用一个新的椒盐噪声判断标准,首先对图像局部各个方向上的灰度值信息进行统计分析,然后利用计算结果判断该点是否为噪声点。实验结果表明,与标准中值滤波算法相比,该算法可以有效地滤除图像中的椒盐噪声,同时还能很好地保留图像的细节。
本文首先介绍了数字图像的基础知识。然后分析了标准中值滤波的实现原理和缺陷不足,并对近几年出现的各种具有代表性的优化中值滤波算法进行了介绍和比较。在此基础上,本文创新性地提出了一种新的优化滤波算法,并描述了其具体实现的方法和步骤,最后给出了相关的计算机仿真实验数据。实验结果表明,该算法与标准中值滤波算法相比,可以有效地检测出噪声点,有更高的信噪比,同时拥有较低的漏检率和误检率,滤波性能更优良。
Whth the development of computer technology, the technologies of image processing gained great interests and wide applications, many new theories and new processing methods were proposed in recent years. Because of communication channel and so on, the signal pixels are always with noise pixels together. Image filter algorithm is always study focus in the field of image processing and analysis, which is still unresolved well till now.
Salt and pepper noise is a kind of common noises which can be eliminated by image filtering algorithms. The standard median filter is one of the most popular nonlinear fiters. Because standard median filter is simple and effective, it was widely used in many domains, but it had a very clear deficiency. The filter effects are influenced by the length of template window. Small template will lead to bad effects and big template will lead to image blurring. On the other hand, all the pixels are replaced with the median value of their neighborhood. Although the noise pixels are replaced, the signal pixels are also replaced that lead to the uncorrect spread of noise.
This paper presents a new improved median-based filtering algorithm to improve standard median filter algorithm. This algorithm gives a new decision criterion. Firstly, this decision citerion calculates the correlation value with its neighbors. And then the value is worked as the measure that we determine whether this pixel is a noise pixel. The simulation experiment shows that this algorithm can protect image signal detail as much as possible when effectively eliminates salt and pepper noise.
Firstly, this paper introduces the basic knowledge of digital image. And then introduces the principle of the standard median filter method, analyzes its deficiency and compares the standard median filter with many other new improved median filters. This paper presents an innovative improved median algorithm, makes a detailed exposition of the implementation method and gives simulation experiment data. At last, the simulation experiment shows that ISM filter can detect noise pixel effectively, get higher SNR and lower omission rate and lower false drop rate. So the ISM algorithm has better filtering performance than standard median filter.
引文
[1]冈萨雷斯数字图像处理[M],北京：电子工业出版社,2006.
[2]邓秀勤,熊勇用于图像处理的加权中值滤波算法[J],计算机技术与发展,2009.3.
[3]邢藏菊,王守觉,邓浩江,罗予晋一种基于极值中值的新型滤波算法[J],中国图象图形学报A辑,2001,6,6：533-536.XING Cang-ju,WANG Shou-jue,DENGHao-jiang, et al. A new filtering algorithm based on extremum and median value[J]. Journal of Image and Graphics,2001,6(6):533-536.
[4]Sun T, Neuvo Y. Detail-preserving median based filters in image processing. Pattern Recognit. Lett.,1994,15:341-347.
[5]Wang Zhou, Zhang David. Progressive switching median filter for the removal of impulse noise from highly corrupted images. IEEE Trans. On Circuits and Systems, II: Analog and Digital Signal Processing,1999,46(1):78-80.
[6]Wang Jung-Hua, Lin Lian-Da. Improved median filter using minmax algorithm for image processing. Electronics Letters,31st July,1997,33(16).
[7]Brownrigg D R K. The weighted median filter. Commun. Ass. Comput. Mach.,1984, 27(8):807～818.
[8]Zhang Xuming, Xu Binshi, Dong Shiyun. Adaptive Median Filtering for Image Processing[J]. Journal of Computer Design & Computer Graphics,2005,17(2):295-299.
[9]Hwang H and Haddad R A. Adaptive median filters:new algorithms and results[J]. IEEE Trans. Image Processing,1995,4:499-502.
[10]D Zhang, Z Wang. Impulse noise detection and removal using fuzzy techniques[J]. Electronics Letters,1997,33(5):373-379.
[11]Z Wang, D Zhang. Restoration of impulse noise corrupted images using long-range correlation[J]. IEEE Signal Processing Letters,1998,5(1):4-6.
[12]Ko S-J, Lee Y H. Center weighted median filters and their applications to image enhancement[J]. IEEE Trans Circuits Syst,1991,38(9):984-993.
[13]Jeong B, Lee Y H. Design of weighted order statistic filter using the perception algorithm[J]. IEEE Transactions on Signal Processing,1994,42(11):3264-3269.
[14]Zhang S and Karim M A. A new impulse detector for switching median filters[J]. IEEE Signal Processing Letters,2002,9:360-363.
[15]飞思科技产品研发中心MATLAB 6.5辅助图像处理[M],北京：电子工业出版社,2003.1.
[16]Bovik A. Handbook of image and video processing[M]. Academic Press,2000.
[17]Pratt W K. Median filtering. Tech. Rep., Image Proc. Institute, Univ. Of Southern California, Los Angeles,1975, Sept.
[18]Pitas I, Venetsanopoulos A N. Order statistics in digital image processing[J]. Proc IEEE,1992,80(12):1893-1921.
[19]张明谦,李雷改进的中值滤波算法[J],自动测量与控制,2007,26(5).
[20]GALLAGHER Jr N C, WISH G L. A theoretical analysis of properties of the median filter[J]. IEEE Trans. On Acoustics Speech, Signal Processing,1981,29(1):1136-1141.
[21]Florencio D A, Schafer R W. Decision-based median filter using local signal statistics[C]. Proc SPIE Vis commum Image Process,1994:268-275.
[22]Pei-Eng Ng, Ma Kai-Kuang. A switching median filter with boundary discriminative noise detection for extremely corrupted images[J]. IEEE Trans Image Process,2006,15(6): 1506-1516.
[23]J-L. Starck et al, Wavelets and Curvelets for image deconvolution:a combined approach, Signal Processing[J].83(2003) 2279-2283.
[24]徐超,陈一虎基于四分法噪声检测的开关中值滤波算法[J],计算机工程与设计,2008,29(18).
[25]张旭阳,徐滨士,董世运,吴毅雄去除脉冲噪声的自适应开关中值滤波[J],光电工程,2006,33(6).
[26]曲延锋,徐健,李卫军,王守觉有效去除图像中脉冲噪声的新型滤波算法[J],计算机辅助设计与图形学学报,2003,15(4).
[27]刘伟,孙丽媛,王汝梅自适应中值滤波在数字图像处理中的应用[J],河北理工大学学报(自然科学版),2007,29(4).
[28]泰然 优化自适应中值滤波器滤除图像椒盐噪声方法研究[J],农业网络信息,2009,2.
[29]Garnett R, Huegerich T, Chui C, et al. A universal noise removal algorithm with an impulse detector[J]. IEEE Trans Image Process,2005,14(11):1747-1754.
[30]Chan R H, Ho C-W and Nikolova M. Convergence of Newton's method for a minimization problem in impulse noise removal[J]. Journal Computational Mathematics, 2004,22:168-177.
[31]Chan R H, Ho C-W and Nikolova M. Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization[J]. IEEE Trans. Image Processing, 2005,14:1479-1485.
[32]SUCHER R. Removal of impulse noise by selective filtering[J]. Proceedings of the IEEE International Conference on Image Processing,1994,2(4):502-506.
[33]ABREU E, LIGHTSTONE M, MITRA S K, et al. A new efficient approach for the removal of impulse noise from highly corrupted image[J]. IEEE Trans. Image Processing, 1996,5(6):1012-1025.
[34]CHEN T, MA K K, CHEN L H. Tri-state median filter for image denoising[J]. IEEE Trans. On Image Process,1999,8(12):1834-1838.
[35]Luo Wenbin, Dang Dung. An efficient method for the removal of impulse noise[C]. Image Processing, IEEE International Confe-rence,2006:2601-2604.
[36]Lee C-S, Hsu C-Y, Kuo Y-H, Intelligent fuzzy image filter for impulse noise removal[C]. Proc IEEE Int Conf Fuzzy Syst,2002:431-436.
[37]Nikovola M. A variational approach to remove outliers and impulse noise[J]. Math Imag Vis,2004,20:99-120.
[38]Pok G, Liu J-C, Nair A S. Selective removal of impulse noise based on homogeneity level information[J]. IEEE Trans Image Processing,2003,12(1):85-92.
[39]How-Lung Eng, Kai-Kuang Ma. Noise adaptive soft-switching median filter[J]. IEEE Trans Image Processing,2001,10(2):242-251.
[40]祝宇鸿,一种改进的数字图像中值滤波算法[J],长春邮电学院报,2001,19(2):23-27. ZHU Yu-hong. An improved median filtering algorithm[J]. Journal of Changchun Post and Telecommunication Institute,2001,19(2):23-27.
[2]邓秀勤,熊勇用于图像处理的加权中值滤波算法[J],计算机技术与发展,2009.3.
[3]邢藏菊,王守觉,邓浩江,罗予晋一种基于极值中值的新型滤波算法[J],中国图象图形学报A辑,2001,6,6：533-536.XING Cang-ju,WANG Shou-jue,DENGHao-jiang, et al. A new filtering algorithm based on extremum and median value[J]. Journal of Image and Graphics,2001,6(6):533-536.
[4]Sun T, Neuvo Y. Detail-preserving median based filters in image processing. Pattern Recognit. Lett.,1994,15:341-347.
[5]Wang Zhou, Zhang David. Progressive switching median filter for the removal of impulse noise from highly corrupted images. IEEE Trans. On Circuits and Systems, II: Analog and Digital Signal Processing,1999,46(1):78-80.
[6]Wang Jung-Hua, Lin Lian-Da. Improved median filter using minmax algorithm for image processing. Electronics Letters,31st July,1997,33(16).
[7]Brownrigg D R K. The weighted median filter. Commun. Ass. Comput. Mach.,1984, 27(8):807～818.
[8]Zhang Xuming, Xu Binshi, Dong Shiyun. Adaptive Median Filtering for Image Processing[J]. Journal of Computer Design & Computer Graphics,2005,17(2):295-299.
[9]Hwang H and Haddad R A. Adaptive median filters:new algorithms and results[J]. IEEE Trans. Image Processing,1995,4:499-502.
[10]D Zhang, Z Wang. Impulse noise detection and removal using fuzzy techniques[J]. Electronics Letters,1997,33(5):373-379.
[11]Z Wang, D Zhang. Restoration of impulse noise corrupted images using long-range correlation[J]. IEEE Signal Processing Letters,1998,5(1):4-6.
[12]Ko S-J, Lee Y H. Center weighted median filters and their applications to image enhancement[J]. IEEE Trans Circuits Syst,1991,38(9):984-993.
[13]Jeong B, Lee Y H. Design of weighted order statistic filter using the perception algorithm[J]. IEEE Transactions on Signal Processing,1994,42(11):3264-3269.
[14]Zhang S and Karim M A. A new impulse detector for switching median filters[J]. IEEE Signal Processing Letters,2002,9:360-363.
[15]飞思科技产品研发中心MATLAB 6.5辅助图像处理[M],北京：电子工业出版社,2003.1.
[16]Bovik A. Handbook of image and video processing[M]. Academic Press,2000.
[17]Pratt W K. Median filtering. Tech. Rep., Image Proc. Institute, Univ. Of Southern California, Los Angeles,1975, Sept.
[18]Pitas I, Venetsanopoulos A N. Order statistics in digital image processing[J]. Proc IEEE,1992,80(12):1893-1921.
[19]张明谦,李雷改进的中值滤波算法[J],自动测量与控制,2007,26(5).
[20]GALLAGHER Jr N C, WISH G L. A theoretical analysis of properties of the median filter[J]. IEEE Trans. On Acoustics Speech, Signal Processing,1981,29(1):1136-1141.
[21]Florencio D A, Schafer R W. Decision-based median filter using local signal statistics[C]. Proc SPIE Vis commum Image Process,1994:268-275.
[22]Pei-Eng Ng, Ma Kai-Kuang. A switching median filter with boundary discriminative noise detection for extremely corrupted images[J]. IEEE Trans Image Process,2006,15(6): 1506-1516.
[23]J-L. Starck et al, Wavelets and Curvelets for image deconvolution:a combined approach, Signal Processing[J].83(2003) 2279-2283.
[24]徐超,陈一虎基于四分法噪声检测的开关中值滤波算法[J],计算机工程与设计,2008,29(18).
[25]张旭阳,徐滨士,董世运,吴毅雄去除脉冲噪声的自适应开关中值滤波[J],光电工程,2006,33(6).
[26]曲延锋,徐健,李卫军,王守觉有效去除图像中脉冲噪声的新型滤波算法[J],计算机辅助设计与图形学学报,2003,15(4).
[27]刘伟,孙丽媛,王汝梅自适应中值滤波在数字图像处理中的应用[J],河北理工大学学报(自然科学版),2007,29(4).
[28]泰然 优化自适应中值滤波器滤除图像椒盐噪声方法研究[J],农业网络信息,2009,2.
[29]Garnett R, Huegerich T, Chui C, et al. A universal noise removal algorithm with an impulse detector[J]. IEEE Trans Image Process,2005,14(11):1747-1754.
[30]Chan R H, Ho C-W and Nikolova M. Convergence of Newton's method for a minimization problem in impulse noise removal[J]. Journal Computational Mathematics, 2004,22:168-177.
[31]Chan R H, Ho C-W and Nikolova M. Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization[J]. IEEE Trans. Image Processing, 2005,14:1479-1485.
[32]SUCHER R. Removal of impulse noise by selective filtering[J]. Proceedings of the IEEE International Conference on Image Processing,1994,2(4):502-506.
[33]ABREU E, LIGHTSTONE M, MITRA S K, et al. A new efficient approach for the removal of impulse noise from highly corrupted image[J]. IEEE Trans. Image Processing, 1996,5(6):1012-1025.
[34]CHEN T, MA K K, CHEN L H. Tri-state median filter for image denoising[J]. IEEE Trans. On Image Process,1999,8(12):1834-1838.
[35]Luo Wenbin, Dang Dung. An efficient method for the removal of impulse noise[C]. Image Processing, IEEE International Confe-rence,2006:2601-2604.
[36]Lee C-S, Hsu C-Y, Kuo Y-H, Intelligent fuzzy image filter for impulse noise removal[C]. Proc IEEE Int Conf Fuzzy Syst,2002:431-436.
[37]Nikovola M. A variational approach to remove outliers and impulse noise[J]. Math Imag Vis,2004,20:99-120.
[38]Pok G, Liu J-C, Nair A S. Selective removal of impulse noise based on homogeneity level information[J]. IEEE Trans Image Processing,2003,12(1):85-92.
[39]How-Lung Eng, Kai-Kuang Ma. Noise adaptive soft-switching median filter[J]. IEEE Trans Image Processing,2001,10(2):242-251.
[40]祝宇鸿,一种改进的数字图像中值滤波算法[J],长春邮电学院报,2001,19(2):23-27. ZHU Yu-hong. An improved median filtering algorithm[J]. Journal of Changchun Post and Telecommunication Institute,2001,19(2):23-27.