堆栈滤波器的研究及应用
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摘要
与线性滤波器相比较，非线性滤波器对于脉冲类、乘性类噪声的滤除，具有
较好的效果，因此近年来受到众多学者的关注。堆栈滤波器是一类非线性数字滤
波器，在数字信号和数字图像处理中有广泛的应用，展开这方面的研究具有实际
意义和应用前景。
堆栈滤波器的特点是具有阈值分解和堆栈特性，这两个重要性质将滤波过程
转化到二进制运算，易于 VLSI 并行实现。本文从理论上具体研究了堆栈滤波器的
原理结构和进行噪声滤除的过程，并通过仿真验证了所给算法的有效性。
本文针对非线性阈值分解结构，进一步结合图像本身的特征，提出了一种新
的动态非线性分解的方法，能够在保证图像信息的同时很大程度上降低滤波过程
的运算量。仿真结果表明，与其它的算法进行比较，本算法具有一定的实用价值。
堆栈滤波器应用于 SAR 图像噪声的去除，也是一个新的尝试。与已有的统计
类滤波算法进行比较，堆栈滤波器也有较好的效果。结合堆栈滤波器的易于集成
实现和并行处理的优点，这部分的研究为开发实时 SAR 图像滤波器提供了一定的
理论基础。
Nonlinear filters do a good job in suppressing impulsive and multiplicative noise
compared with linear filters. So they are widely used in digital signal processing and
image processing and worthy of research.
Stack filters are a class of nonlinear digital filters possessing threshold
decomposition and stacking property. These two important properties ensure that the
filtering go on in binary filed only with easy comparison, addition and multiplication,
which allow an efficient VLSI implementation. This paper studies the architecture and
theory of stack filters and the adaptive algorithms for designing stack filters. Some
results of simulation for the proposed algorithms are given to prove their validity.
Then a new nonlinear threshold decomposition architecture is introduced to reduce
the complexity of algorithms. By combining with the character of image, a dynamic
nonlinear decomposition architecture is proposed to implement stack filters which can
shorten the running time in the filtering procedure and improve the quality of the output
image simultaneously. Comparisons on some criterion between this new algorithm and
others are provided to show the validity of our algorithm.
Results of the innovative application on SAR images filtering are given in the end,
which show that stack filters are approximately with noise filtering algorithms based on
local statistics property. And as their superior in integration implement, researches in
this part supply for exploring the real time SAR filters.
较好的效果，因此近年来受到众多学者的关注。堆栈滤波器是一类非线性数字滤
波器，在数字信号和数字图像处理中有广泛的应用，展开这方面的研究具有实际
意义和应用前景。
堆栈滤波器的特点是具有阈值分解和堆栈特性，这两个重要性质将滤波过程
转化到二进制运算，易于 VLSI 并行实现。本文从理论上具体研究了堆栈滤波器的
原理结构和进行噪声滤除的过程，并通过仿真验证了所给算法的有效性。
本文针对非线性阈值分解结构，进一步结合图像本身的特征，提出了一种新
的动态非线性分解的方法，能够在保证图像信息的同时很大程度上降低滤波过程
的运算量。仿真结果表明，与其它的算法进行比较，本算法具有一定的实用价值。
堆栈滤波器应用于 SAR 图像噪声的去除，也是一个新的尝试。与已有的统计
类滤波算法进行比较，堆栈滤波器也有较好的效果。结合堆栈滤波器的易于集成
实现和并行处理的优点，这部分的研究为开发实时 SAR 图像滤波器提供了一定的
理论基础。
Nonlinear filters do a good job in suppressing impulsive and multiplicative noise
compared with linear filters. So they are widely used in digital signal processing and
image processing and worthy of research.
Stack filters are a class of nonlinear digital filters possessing threshold
decomposition and stacking property. These two important properties ensure that the
filtering go on in binary filed only with easy comparison, addition and multiplication,
which allow an efficient VLSI implementation. This paper studies the architecture and
theory of stack filters and the adaptive algorithms for designing stack filters. Some
results of simulation for the proposed algorithms are given to prove their validity.
Then a new nonlinear threshold decomposition architecture is introduced to reduce
the complexity of algorithms. By combining with the character of image, a dynamic
nonlinear decomposition architecture is proposed to implement stack filters which can
shorten the running time in the filtering procedure and improve the quality of the output
image simultaneously. Comparisons on some criterion between this new algorithm and
others are provided to show the validity of our algorithm.
Results of the innovative application on SAR images filtering are given in the end,
which show that stack filters are approximately with noise filtering algorithms based on
local statistics property. And as their superior in integration implement, researches in
this part supply for exploring the real time SAR filters.
引文
[1] 阮秋琦. 数字图像处理学. 北京：电子工业出版社，2001.1。
[2] 张兆礼，赵春晖，梅晓丹. 现代图像处理技术及 Matlab 实现. 北京：人民邮电
出版社，2001.11。
[3] 张毓晋. 图象处理和分析. 北京：清华大学出版社，1999.3。
[4] 陈贺新. 非线性滤波器与数字图像处理. 北京：国防工业出版社，1997.3
[5] Wiener N. Nonlinear Problems in Random Theory. New York: The Technology
Press, MIT and John Wiley and Sons, Inc. 1958
[6] Tukey J.W. Exploratory Data Analysis, Addison-Wesley: 1977.
[7] C. Bounsaythip, J. T. Alander, “Genetic algorithms in image processing – A
review,” Proceedings of the 3NWGA, Helsinki, Finland, 20-22, Aug.1997,
pp.173~192
[8] J. P. Fitch，E. J. Coyle，and N. C. Gallagher，Jr.，“Median filtering by threshold
decomposition，”IEEE Trans. Acoust.，Speech, Signal Processing, vol. ASSP-32, pp.
1183-1188, Dec. 1984.
[9] ____，“Median filtering by threshold decomposition,” IEEE Trans. Acoust., Speech,
Signal Processing. vol. ASSP-32. May 1985.
[10]P. D. Wendt, E. J. Coyle, and N. C. Gallagher, Jr., “Stack Filters,” IEEE Trans.
Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 898-911, Aug. 1986.
[11]J. P. Fitch. “Software and VLSI algorithms for generalized rank order filtering,”
UCRL Res. Rep. 92674, Lawrence Livermore Lab., Livermore, CA, Mar. 1985；and
IEEE Trans. Circuits Syst.. vol, CAS-34, May 1987.
[12]张祥光. 非线性理论在图像抑噪中的应用研究（硕士论文）. 甘肃：兰州大学，
2002。
[13]V.Krishnan, “Nonlinear Filtering and Smoothing: An Introduction to Martingales,
Stochastic Integrals and Estimation,” New York: Wiley, 1984
[14]Palmieri F. and Boncelet Jr.C.G. “A class of nonlinear adaptive filters,” On Proc.
IEEE Int. Conf. On Acoust., Speech and Signal Processing, New York,
pp.1483-1486,1988。
[15]沈福民.自适应信号处理.西安电子科技大学.2001.3。
[16]Lin Yin, Jaakko T. Astola, Y. A. Neuvo, “Adaptive stack filtering with application to
image processing,” IEEE Trans. Signal Processing, vol. 41, No. 1, Jan.1993, pp.
162~183.
[17]Edward J. Coyle, Jean-Hsang Lin, “Stack filters and the mean absolute error
参考文献 45
criterion,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. 36, No. 8, Aug.
1988, pp. 1244~1254.
[18]J. H. Lin, T. M. Sellke, and E. J. Coyle, “Adaptive stack filtering under the mean
absolute error criterion,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38,
June,1990, pp. 938~954.
[19]J. H. Lin and Y. T. Kim, “Fast algorithm for training stack filters,” IEEE Trans.
Signal Processing, vol. 42, Apr. 1994, pp. 772~781.
[20]Jisang Yoo, Kelvin L. Fong, Jr-Jen Huang, et., “A fast algorithm for designing stack
filters,” IEEE transactions on image processing, Vol.8, No.8, Aug.1999,
pp.1014~1028.
[21]Win-Long Lee, Kuo-Chin Fan, and Zhi-Ming Chen, “Design of optimal stack filters
under the MAE criterion,” IEEE Trans. Signal Processing, vol.47, No.12, Dec.
1999, pp. 3345~3354
[22]Pao-Ta Yu, “Some presentation properties of stack filters,” IEEE Trans. Signal
Processing, vol.40, No.9, Sep. 1992, pp. 2261~2265.
[23]Chin-Chuan Han and Kuo-Chin Fan, “Finding of optimal stack filter by graphic
searching methods,” IEEE Trans. Signal Processing, vol. 45, No.7, July 1997, pp.
1857~1862.
[24]K. K. Delibasis, P. E. Undrill, G. G. Cameron, “Genetic algorithm implementation
of stack filter design for image restoration,” IEE Proc.-Vis. Image Signal Process.,
Vol. 143, No. 3, June 1996, pp. 177~183
[25]刘忠仁，孙圣和. 基于模糊神经网络的脉冲噪声滤波器.《中国图象图形学报》，
2001 年第 4 期。
[26]J.-H. Lin, Y. T. Kim, and G. Soemarwoto, “Nonlinear filtering techniques based on
a new threshold decomposition architecture,” in Proc. 26th Ann. Conf. Information
Science and Systems, Princeton, NJ, Mar. 18-20, 1992.
[27]J.-H. Lin, Nirwan Ansari, Jinhui Li, “Nonlinear Filtering by Threshold
Decomposition,” IEEE Trans. Image Processing, vol. 8,No.7, July. 1999.
[28]张薇，沈允春，张曙，“堆栈滤波的递归实现，”中国图象图形学报（A 版），
第 5 卷第 10 期，2000 年 10 月，pp851~856.
[29]G. R. Arce and J. L. Paredes, “Recursive weighted median filters admitting negative
weights and their optimization,” IEEE Trans. Signal Processing, vol. 48, Mar.
2000, pp. 768-779.
[30]J. L. Paredes and G. R. Arce, “Stack filters, stack smoothers, and mirrored threshold
decomposition,” IEEE Trans. Signal Processing, vol. 47, Oct. 1999, pp. 2757-2767
46 堆栈滤波器的研究及应用
[31]Ilya Shmulevich, et al “Output Distributions of stack filters based on Mirrored
Threshold Decomposition,” IEEE Trans. Signal Processing, vol.49, No.7, July 2001,
pp.1454~1460
[32]J. L. Paredes and Gonzalo R. Arce, “Optimization of stack filters based on mirrored
threshold decomposition,” IEEE Trans. Signal Processing, vol.49, No.6, July 2001,
pp.1179~1188.
[33]R. G. Harber, S. C. Bass, and G. L. Neudeck, “VLSI implementation of a fast
rank-order algorithm,” in Proc. ICASSP’85, Tampa, FL, Mar.1985
[34]S. Muroga, “Threshold logic and its applications,” New York: Wiley, 1971.
[35]C. R. Baugh, “Bounds on the number of pseudo threshold functions,” IEEE Trans.
Comput., vol. C-20, 1971, pp. 1602~1605.
[36]李树涛，王耀男. 图像椒盐噪声的非线性自适应滤除. 中国图象图形学报，2000
年第 12 期。
[37]王伟，赵春晖，孙圣和. 基于层叠处理的多级自适应 WOS 滤波器. 中国图象
图形学报，2000 年第 8 期。
[38]赵春晖，惠俊英，王伟，孙圣和. 一类自适应顺序形态滤波器. 中国图象图形
学报，2000 年第 8 期。
[39]E. J. Coyle, J. –H. Lin, and M. Gabbouj, “Optimal stack filtering and estimation
and structural approaches to image processing,” IEEE Trans. Acoust., Speech,
Signal Processing, vol. 37, No. 12, Dec.1989
[40]王伟，孙圣和，赵春晖，“基于 Hasse 图的层叠滤波器正布尔函数生成算法”，
哈尔滨工业大学学报，第 32 卷第 1 期，2000 年 2 月，pp.34~36。
[41]Jong-Sen Lee, “Digital image enhancement and noise filtering by use of local
statistics,” IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. PAMI-2,
No. 2, Mar. 1980, pp. 165~168.
[42]Jong-Sen Lee, “Speckle analysis and smoothing of synthetic aperture radar
images,” Computer graphics and image processing, 1981, 17, pp. 24~32.
[43]Jong-Sen Lee, Jurkevich I. “Speckle filtering of synthetic aperture radar images: A
review,” Remote Sensing Reviews, Aug. 1994, pp. 313~340.
[44]D. T. kuan, A. A. Sawchuk, “Adaptive noise smoothing filter for signal-dependent
noise,” IEEE Trans. on PAMI., 1985, Vol.7, No.2, pp. 165～177.
[45]Victor S. Frost, Josephine Abbott Stiles, “A model for radar images and its
application to adaptive digital filtering of multiplicative noise,” IEEE Trans. on
PAMI., 1982, Vol.4, No. 2,pp. 157~165.
[46]T. R. Crimmins, “Geometric filter for reducing speckle,” Appl. Opt., 1985, Vol. 24,
参考文献 47
pp. 1438~1443.
[47]Lopes A.,Touzi R., “Adaptive speckle filters and scene heterogeneity,” IEEE Trans.
on Geosci. And Remote Sensing, 1990A, Vol. 28, No. 6, pp.992~1000
[48]Lopes A., Nezry E, Touzi R, “Maximum a posteriori speckle filtering and first order
texture model in SAR images,” Proceeding of the IGASS’90, 1990,pp. 2409~2412.
[49]Lopes A., Nezry E, Touzi R. “Structure detection and statistical adaptive speckle
filters in SAR images,” Int. J. Remote Sensing, 1993, Vol.14, No.9, pp. 1735~1758.
[50]陈东等，SAR 图像斑点噪声消除算法的研究，红外与激光工程，2000.8 第 29
卷第 4 期，pp. 9~12
[51]邓炜，赵荣椿，基于小波变换的 SAR 图像相干斑噪声消除方法研究，信号处
理，第 17 卷第 1 期，2001.2，pp.86~91
[2] 张兆礼，赵春晖，梅晓丹. 现代图像处理技术及 Matlab 实现. 北京：人民邮电
出版社，2001.11。
[3] 张毓晋. 图象处理和分析. 北京：清华大学出版社，1999.3。
[4] 陈贺新. 非线性滤波器与数字图像处理. 北京：国防工业出版社，1997.3
[5] Wiener N. Nonlinear Problems in Random Theory. New York: The Technology
Press, MIT and John Wiley and Sons, Inc. 1958
[6] Tukey J.W. Exploratory Data Analysis, Addison-Wesley: 1977.
[7] C. Bounsaythip, J. T. Alander, “Genetic algorithms in image processing – A
review,” Proceedings of the 3NWGA, Helsinki, Finland, 20-22, Aug.1997,
pp.173~192
[8] J. P. Fitch，E. J. Coyle，and N. C. Gallagher，Jr.，“Median filtering by threshold
decomposition，”IEEE Trans. Acoust.，Speech, Signal Processing, vol. ASSP-32, pp.
1183-1188, Dec. 1984.
[9] ____，“Median filtering by threshold decomposition,” IEEE Trans. Acoust., Speech,
Signal Processing. vol. ASSP-32. May 1985.
[10]P. D. Wendt, E. J. Coyle, and N. C. Gallagher, Jr., “Stack Filters,” IEEE Trans.
Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 898-911, Aug. 1986.
[11]J. P. Fitch. “Software and VLSI algorithms for generalized rank order filtering,”
UCRL Res. Rep. 92674, Lawrence Livermore Lab., Livermore, CA, Mar. 1985；and
IEEE Trans. Circuits Syst.. vol, CAS-34, May 1987.
[12]张祥光. 非线性理论在图像抑噪中的应用研究（硕士论文）. 甘肃：兰州大学，
2002。
[13]V.Krishnan, “Nonlinear Filtering and Smoothing: An Introduction to Martingales,
Stochastic Integrals and Estimation,” New York: Wiley, 1984
[14]Palmieri F. and Boncelet Jr.C.G. “A class of nonlinear adaptive filters,” On Proc.
IEEE Int. Conf. On Acoust., Speech and Signal Processing, New York,
pp.1483-1486,1988。
[15]沈福民.自适应信号处理.西安电子科技大学.2001.3。
[16]Lin Yin, Jaakko T. Astola, Y. A. Neuvo, “Adaptive stack filtering with application to
image processing,” IEEE Trans. Signal Processing, vol. 41, No. 1, Jan.1993, pp.
162~183.
[17]Edward J. Coyle, Jean-Hsang Lin, “Stack filters and the mean absolute error
参考文献 45
criterion,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. 36, No. 8, Aug.
1988, pp. 1244~1254.
[18]J. H. Lin, T. M. Sellke, and E. J. Coyle, “Adaptive stack filtering under the mean
absolute error criterion,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38,
June,1990, pp. 938~954.
[19]J. H. Lin and Y. T. Kim, “Fast algorithm for training stack filters,” IEEE Trans.
Signal Processing, vol. 42, Apr. 1994, pp. 772~781.
[20]Jisang Yoo, Kelvin L. Fong, Jr-Jen Huang, et., “A fast algorithm for designing stack
filters,” IEEE transactions on image processing, Vol.8, No.8, Aug.1999,
pp.1014~1028.
[21]Win-Long Lee, Kuo-Chin Fan, and Zhi-Ming Chen, “Design of optimal stack filters
under the MAE criterion,” IEEE Trans. Signal Processing, vol.47, No.12, Dec.
1999, pp. 3345~3354
[22]Pao-Ta Yu, “Some presentation properties of stack filters,” IEEE Trans. Signal
Processing, vol.40, No.9, Sep. 1992, pp. 2261~2265.
[23]Chin-Chuan Han and Kuo-Chin Fan, “Finding of optimal stack filter by graphic
searching methods,” IEEE Trans. Signal Processing, vol. 45, No.7, July 1997, pp.
1857~1862.
[24]K. K. Delibasis, P. E. Undrill, G. G. Cameron, “Genetic algorithm implementation
of stack filter design for image restoration,” IEE Proc.-Vis. Image Signal Process.,
Vol. 143, No. 3, June 1996, pp. 177~183
[25]刘忠仁，孙圣和. 基于模糊神经网络的脉冲噪声滤波器.《中国图象图形学报》，
2001 年第 4 期。
[26]J.-H. Lin, Y. T. Kim, and G. Soemarwoto, “Nonlinear filtering techniques based on
a new threshold decomposition architecture,” in Proc. 26th Ann. Conf. Information
Science and Systems, Princeton, NJ, Mar. 18-20, 1992.
[27]J.-H. Lin, Nirwan Ansari, Jinhui Li, “Nonlinear Filtering by Threshold
Decomposition,” IEEE Trans. Image Processing, vol. 8,No.7, July. 1999.
[28]张薇，沈允春，张曙，“堆栈滤波的递归实现，”中国图象图形学报（A 版），
第 5 卷第 10 期，2000 年 10 月，pp851~856.
[29]G. R. Arce and J. L. Paredes, “Recursive weighted median filters admitting negative
weights and their optimization,” IEEE Trans. Signal Processing, vol. 48, Mar.
2000, pp. 768-779.
[30]J. L. Paredes and G. R. Arce, “Stack filters, stack smoothers, and mirrored threshold
decomposition,” IEEE Trans. Signal Processing, vol. 47, Oct. 1999, pp. 2757-2767
46 堆栈滤波器的研究及应用
[31]Ilya Shmulevich, et al “Output Distributions of stack filters based on Mirrored
Threshold Decomposition,” IEEE Trans. Signal Processing, vol.49, No.7, July 2001,
pp.1454~1460
[32]J. L. Paredes and Gonzalo R. Arce, “Optimization of stack filters based on mirrored
threshold decomposition,” IEEE Trans. Signal Processing, vol.49, No.6, July 2001,
pp.1179~1188.
[33]R. G. Harber, S. C. Bass, and G. L. Neudeck, “VLSI implementation of a fast
rank-order algorithm,” in Proc. ICASSP’85, Tampa, FL, Mar.1985
[34]S. Muroga, “Threshold logic and its applications,” New York: Wiley, 1971.
[35]C. R. Baugh, “Bounds on the number of pseudo threshold functions,” IEEE Trans.
Comput., vol. C-20, 1971, pp. 1602~1605.
[36]李树涛，王耀男. 图像椒盐噪声的非线性自适应滤除. 中国图象图形学报，2000
年第 12 期。
[37]王伟，赵春晖，孙圣和. 基于层叠处理的多级自适应 WOS 滤波器. 中国图象
图形学报，2000 年第 8 期。
[38]赵春晖，惠俊英，王伟，孙圣和. 一类自适应顺序形态滤波器. 中国图象图形
学报，2000 年第 8 期。
[39]E. J. Coyle, J. –H. Lin, and M. Gabbouj, “Optimal stack filtering and estimation
and structural approaches to image processing,” IEEE Trans. Acoust., Speech,
Signal Processing, vol. 37, No. 12, Dec.1989
[40]王伟，孙圣和，赵春晖，“基于 Hasse 图的层叠滤波器正布尔函数生成算法”，
哈尔滨工业大学学报，第 32 卷第 1 期，2000 年 2 月，pp.34~36。
[41]Jong-Sen Lee, “Digital image enhancement and noise filtering by use of local
statistics,” IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. PAMI-2,
No. 2, Mar. 1980, pp. 165~168.
[42]Jong-Sen Lee, “Speckle analysis and smoothing of synthetic aperture radar
images,” Computer graphics and image processing, 1981, 17, pp. 24~32.
[43]Jong-Sen Lee, Jurkevich I. “Speckle filtering of synthetic aperture radar images: A
review,” Remote Sensing Reviews, Aug. 1994, pp. 313~340.
[44]D. T. kuan, A. A. Sawchuk, “Adaptive noise smoothing filter for signal-dependent
noise,” IEEE Trans. on PAMI., 1985, Vol.7, No.2, pp. 165～177.
[45]Victor S. Frost, Josephine Abbott Stiles, “A model for radar images and its
application to adaptive digital filtering of multiplicative noise,” IEEE Trans. on
PAMI., 1982, Vol.4, No. 2,pp. 157~165.
[46]T. R. Crimmins, “Geometric filter for reducing speckle,” Appl. Opt., 1985, Vol. 24,
参考文献 47
pp. 1438~1443.
[47]Lopes A.,Touzi R., “Adaptive speckle filters and scene heterogeneity,” IEEE Trans.
on Geosci. And Remote Sensing, 1990A, Vol. 28, No. 6, pp.992~1000
[48]Lopes A., Nezry E, Touzi R, “Maximum a posteriori speckle filtering and first order
texture model in SAR images,” Proceeding of the IGASS’90, 1990,pp. 2409~2412.
[49]Lopes A., Nezry E, Touzi R. “Structure detection and statistical adaptive speckle
filters in SAR images,” Int. J. Remote Sensing, 1993, Vol.14, No.9, pp. 1735~1758.
[50]陈东等，SAR 图像斑点噪声消除算法的研究，红外与激光工程，2000.8 第 29
卷第 4 期，pp. 9~12
[51]邓炜，赵荣椿，基于小波变换的 SAR 图像相干斑噪声消除方法研究，信号处
理，第 17 卷第 1 期，2001.2，pp.86~91