α稳定分布及其在斑点抑制中的应用研究

摘要/Abstract

摘要： 稳定分布是高斯分布、Rayleigh分布等的广义形式,可以准确描述脉冲型数据,在SAR图像、超声图像、遥感图像的噪声抑制方面具有显著效果和广泛的应用,是成像领域的研究热点。但目前关于α稳定分布性质、参数估计及降噪研究尚未有综合的阐述,缺少系统性的分析。从传统的滤波方法,特别是基于MAP方法的滤波算法开始,结合当今的热点研究,即相干斑抑制,综合介绍了α稳定分布的定义、特征函数、极限性质及特殊分布形式(对称α分布(SαS)、拖尾Rayleigh分布、高斯分布、混合分布等),阐述和分析了一些现有的参数估计原理和方法。最后,开展了滤噪对比试验,验证了MAP滤波方法的有效性。同时,对当前最新的相干斑抑制应用做了较为系统的总结。同时,在第1节介绍了SAR图像相干斑的产生和统计特性、经典的相干斑滤除算法、流行的非局部平均方法的原理。

关键词: 相干斑抑制,α稳定分布,拖尾分布,乘性噪声,MAP滤波器中图法分类号TP391.41文献标识码A

Abstract: stable distributions are the generalization forms of Gaussian distribution and Rayleigh distribution,capacity of accurately describing impulsive data and have widely applications in imaging and noise suppression．However,there are still lack of comprehensive introduction and comparative analysis in this aspect．Associating with current hot research points in speckle suppression and departing from MAP based filtering approaches,this paper introduces the definition,characteristic functions and properties of α stable distributions and their special forms including symmetrical α distribution,generalized Rayleigh distribution,Gauss distribution and some kinds of mixture distributions,and then analyzes some useful parameter estimation principles and methods．Subsequently,an experimental comparison was carried out and it verifies the superiority of MAP based filter．Besides,this paper introduces the newest applications in speckle suppression of these distributions．At the same time,this paper summaries the statistical characteristics of speckle and discusses some commonly used noise filtering algorithms,such as non-local mean approach．

Key words: Speckle suppression,Alpha stable distribution,Heavy tailed distribution,Multiplicative noise,MAP based filter

管涛,牛晓太. α稳定分布及其在斑点抑制中的应用研究[J]. 计算机科学, 2014, 41(Z6): 196-202. https://doi.org/

GUAN Tao and NIU Xiao-tai. Study on α Stable Distributions and Speckle Suppression[J]. Computer Science, 2014, 41(Z6): 196-202. https://doi.org/

参考文献

[1] Marshall J S,Hitschfeld W．Interpretation of the fluctuatingecho from random distributed scatters,part I[J]．Canadian Journal of Physics,1953,31(6):962-994
[2] Oliver C,Quegan S．合成孔径雷达图像理解[M].北京:电子工业出版社,2009
[3] Buades A,Coll B,Morel A M．Image denoising methods．A new nonlocal principle[J]．SIAM Review,2010,52(1):113-147
[4] 韩春明,郭华东,王长林.SAR图像斑点噪声抑制的本质[J].遥感学报,2002,6(6):470-474)
[5] Touzi R．A review of speckle filtering in the context of estimation theory[J]．IEEE Transactions on Geoscience and Remote Sensing,2002,40(11):2392-2405
[6] Lee J S,Wen J H,et al．Improved sigma filter for speckle filtering of SAR imagery[J]．IEEE Transactions on Geoscience and Remote Sensing,2009,47(1):202-213
[7] Lee J S．Digital image enhancement and noise filtering by use of local statistics[J]．IEEE Transactions on Pattern Analysis and Machine Intelligence,1980,PAMI-2(2):165-169
[8] Kuan D T,Sawchuk A A,Strand T C．Adaptive noise smoothingfilter for images with signal-dependent noise[J]．IEEE Transactions on Pattern Analysis and Machine Intelligence,1985,7(2):165-178
[9] Lopes A,Tonzi R,Nezry E．Adaptive speckle filter and sense heterogeneity[J]．IEEE Transactions on Geoscience and Remote Sensing,1990,28(6):992-1000
[10] Yu Y,Acton S T．Speckle reducing anisotropic diffusion[J]．IEEE Transactions on Image Processing,2002,11(11):12602-1270
[11] 李灿飞,王耀南,肖昌炎,等．用于超声斑点噪声滤波的各向异性扩散新模型[J].自动化学报,2012,8(3):412-419
[12] Lopes A,Nezry E,TouziR,et al．Structure detection and statistical adaptive speckle filtering in SAR images [J]．International Journal of Remote Sensing,1993,14(9):1735-1758
[13] Baraldi A,Parmiggiani F．A refined gamma MAP SAR speckle filter with improved geometrical adaptivity[J]．IEEE Transactions on Geoscience and Remote Sensing,1995,33(5):1245-1257
[14] Kuruoglu E E,Zerubia J．Modeling SAR images with a genera-lization of the Rayleigh distribution[J]．IEEE Transactions on Image Processing,2004,13(4):527-534
[15] 孙增国,韩崇昭．拖尾Rayleigh分布:基本性质及其应用[J].自动化学报,2008,34(9):1067-1075
[16] Coupe P,Yger P,Prima S,et al．An optimized blockwise non local means denoising filter for 3D magnetic resonance images[J]．IEEE Transactions on Medical Imaging,2008,7(4):425-441
[17] Coupe P,Hellier P,Kervrann C,et al．NonLocal Means-based Speckle Filtering for Ultrasound Images[J]．IEEE Transactions on Image Processing,2009,18(10):2221-2229
[18] Brox T,Kleinschmidt O,Cremers D．Efficient nonlocal meansfor denoising of textural patterns[J]．IEEE Transactions on Ima-ge Processing,2008,17(7):1083-1092
[19] Zhang Xu-ming,Zhan Yi,Ding Ming-yue,et al．Decision-based non-local means filter for removing impulse noise from digital images[J]．Signal Processing,2013,93:517-524
[20] 杨学志,沈晶,范良欢．基于非局部均值滤波的结构保持相干斑噪声抑制方法[J].中国图象图形学报,2009,4(12):2443-2450
[21] Nikias C L,Shao M．Signal Processing with Alpha-Stable Distributions and Applications[M]．New York:Wiley,1995
[22] Samoradnitsky G,Taqqu M S．Stable Non-Gaussian RandomProcesses[M]．New York:Chapman and Hall,CRC,1994
[23] Gradshteyn S I,Ryzhik I M．Table of Integrals,Series,and Pro-ducts[M]．New York:Academic,1965
[24] Brorsen B W,Yang S R．Maximum likelihood estimates of symmetric stable distribution parameters[J]．Statistics -Simulation and Computation,1990,19(4):1459-1464
[25] Zolotarev V M．Integral transfomations of distributions and estimates of parameters of multidimensional spherically symme-tric stable laws[M]∥ Gani J,Rohatgi V K,eds． Contribution to Probability:A Collection of Papers Dedicated to Eugene Lukacs．New York Academic,1981:283-305
[26] Georgiou P G,Tsakalides P,Kyriakakis C．Alpha-stable mode-ling of noise and robust time-delay estimation in the presence of impulsive noise[J]．IEEE Transactions on Multimedia,1999,1(3):291-302
[27] Abramowitz M,Stegun I A．Handbook of Mathematical Functions[M]．Dover,New York,1972
[28] Ma X,Nikias C L．Parameter estimation and blind channel identification in impulsive signal environments[J]．IEEE Transactions on Signal Processing,1995,43(12):2884-2897
[29] 管涛,李玲玲.高斯混合模型、求解算法及视觉应用综述[J].中国图象图形学报,2012,7(12):1461-1471
[30] Bodenschatz J S,Nikias C L．Maximum-likelihood symmetric α-stable parameter estimation[J]．IEEE Transactions on Signal Processing,1999,47(5):1382-1285
[31] DuMouchel W H．Stable Distributions in Statistical Inference[D]．Yale University,Department of Statistics,1971
[32] DuMouchel W H．On the asymptotic normality of the maximum-likelihood estimate when sampling from a stable distribution[J]．The Annals of Statistics,1973,1(5):948-957
[33] Andrews B,Calder M,Davis R A．Maximum likelihood estimation for α-stable autoregressive processes[J]．The Annals of Statistics,2009,37(4):1946-1982
[34] Mittnik S,Rachev S T,Doganoglu T,et al．Maximum likelihood estimation of stable Paretian models[J]．Mathematical and Computer Modelling,1999,29(10-12):275-293
[35] Aysal T C,Barner K E．Rayleigh-Maximum-Likelihood filtering for speckle reduction of ultrasound images[J]．IEEE Transactions Medical Imaging,2007,26(5):712-727
[36] Godsill S．MCMC and EM-based methods for inference in heavy-tailed processes with alpha-stable innovations[C]∥Proceeding of the IEEE Signal Processing Workshop on Higher-Order Staticstics.1999:228-232
[37] Szajnowski W J,Wynne J B．Simulation of dependent samples of symmetric alpha-stable clutter[J]．IEEE Signal Processing Letters,2001,8(5):151-152
[38] Givens G H,Hoeting J A．Computational Statistics[M]．Beijing:Posts & Telecom Press,2008
[39] Buckle D J．Bayesian inference for stable distributions[J]．Journal of American Statistical Association,1995,90(430):605-613
[40] Salas-Gonzalez D,Kuruoglu E E,Ruiz D P．Modelling with mixture of symmetric stable distributions using Gibbs sampling[J]．Signal Processing,2010,90(3):774-783
[41] Lombardi M J．Bayesian inference for α -stable distributions:A random walk MCMC approach[J]．Computational Statistics & Data Analysis-CS&DA,2007,51(5):2688-2700
[42] Fama E F,Roll R．Parameter estimates for symmetric stable dis-tributions[J]．Journal of the American Statistical Association,1971,66(334):331-338
[43] Press S J．Estimation of univariate and multivariate stable distributions[J]．Journal of the American Statistical Association,1972,67(340):842-846
[44] Kuruoglu E E．Density parameter estimation of skewed α-stable distributions[J]．IEEE Transactions on Signal Processing,2001,49(10):2192-2201
[45] Moser G,Zerubia J,Serpico S B．Dictionary-based stochastic expectation maximization for SAR amplitude probability density function estimation[J]．IEEE Transactions on Geoscience and Remote Sensing,2006,44(1):188-200
[46] Bates S,McLaughlin S．The estimation of stable distribution parameters from teletraffic data[J]．IEEE Transactions on Signal Processing,2000,48(3):865-871
[47] Tsihrintzis G A,Nikias C L．Performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha-stable process[J]．IEEE Transactions on Communications,1995,43(2):904-914
[48] 王梓坤．概率论基础及其应用[M]．北京:科学出版社,1976
[49] Xie Hua,Pierce L E,Ulaby F T．Statistical Properties of Logarithmically Transformed Speckle[J]．IEEE Transactions on Geoscience and Remote Sensing,2002,40(3):721-727
[50] Andrews D F,Mallows C L．Scale Mixtures of normal distributions．Journal of the Royal Statistical Society[J]．Series B (Methodological),1974,36(1):99-102
[51] West M．On scale mixtures of normal distributions[J]．Biometrika,1987,74(3):646-648
[52] Yu Cheng-pu,Zhangm Ci-shen,Xie Li-hua．A multiplicative Nakagami speckle reduction algorithm for ultrasound images[J]．Multidimensional Systems and Signal Processing,2012,23(4):499-513
[53] Kuruoglu E E,Molina C,Fitzgerald W J．Approximation of a-stable probability densities using finite Gaussian mixtures[C]∥The 9th European Signal Processing Conference:Theories and Applications．Rhodes,Greece,1998:989-992
[54] Jakeman E,Pusey P N．Significance of K distributions in scat-tering experiments[J]．Physical Review Letters,1978,0:546-550
[55] Salas-Gonzalez D,Kuruoglu E E,Ruiz D P．Finite mixture of α-stable distributions [J]．Digital Signal Processing,2009,9(2):250-264
[56] Sangston K J,Gerlach K R．Coherent detection of radar targets in a non-Gaussian background[J]．IEEE Transactions on Aerospace and Electronic Systems,1994,30(2):330-340
[57] Achim A M,Kuruoglu E E,Zerubia J．SAR image filtering basedon the heavy-tailed Rayleigh model[J]．IEEE Transactions on Image Processing,2006,15(9):2686-2693
[58] Kozick R J,Sadler B M．Maximum-likelihood array processing in non-Gaussian noise with Gaussian mixtures[J]．IEEE Transactions on Signal Processing,2002,48(12):3520-3535
[59] 白静,侯彪,王爽,等.基于提升Direction-let域高斯混合尺度模型的SAR图像噪声抑制[J]．计算机学报,2008,1(7):1234-1241
[60] 李旭涛,王首勇,金连文．应用Alpha稳定分布对雷达杂波的辨识[J].电子与信息学报,2008,0(9):2042-2046
[61] Kuruoglu E E,Zerubia J．Skewed alpha-stable distributions for modeling textures [J]．Pattern Recognition Letters,2003,24(1):339-348
[62] Tsionas E G．Monte carlo inference in econometric models with symmetric stable disturbances[J]．Journal of Econometrics,1998,88(2):365-401

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed