基于小波变换的合成孔径雷达图像降噪
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摘要
合成孔径雷达(SAR)成像系统诞生于上世纪50-60年代。SAR成像系统最重要的特点之一是能够在全天候的条件下对大面积区域生成高分辨率的图像,因而广泛应用于高质量遥感制图、地球表面监控、搜索与救援、矿藏探测以及自动目标识别等诸多领域。
合成孔径雷达成像的主要问题是生成的图像一般都会受到乘性斑点噪声的干扰。这是由于形成图像的背向散射电磁波相干造成的。SAR图像中的斑点噪声掩盖了图像细节,在视觉上降低了图像质量,并且会严重影响自动场景分割和目标识别的效果。由于SAR图像斑点噪声的成因比较特殊,一般的数字图像处理中所采用的降噪方法对SAR图像并不十分有效。所以,降低和抑制SAR图像的斑点噪声一直以来都是SAR图像研究的一个热点。
SAR图像降噪的要求,是在滤除噪声的同时,尽量保持原始图像的边缘和纹理等细节信息。科研人员根据SAR斑点噪声的性质和特点,已经提出了多种空间域自适应滤波器。而本文则是从多分辨率分析的角度出发,将小波变换这一强大的数学工具应用于SAR图像降噪。
本文首先简要介绍了合成孔径雷达成像原理,以及SAR图像的巨大作用。然后,简单地分析了SAR图像斑点噪声的形成原因和统计模型,接着大致描述了小波和多分辨率分析的基本原理。在这些背景知识的基础上,本文分析了SAR图像小波系数的分布特点,然后将经典的小波域自适应软阈值法应用于降低SAR图像斑点噪声。进一步,本文提出根据小波系数的局部统计量选取阈值以及估计相关参数的方法。对真实的SAR图像的实验结果表明,本文算法在降低噪声和保持边缘纹理细节之间取得了较好的平衡,处理后的SAR图像的视觉效果和质量评估参数都要优于传统的空间域滤波方法的处理结果。最后,本文深入分析了小波变换和多分辨率分析对于SAR图像降噪的意义,提出了将来可进一步深入研究的方向。
Synthetic aperture radar (SAR) imaging system was invented in the 50s and 60s of 20th century. One of the most important features of SAR imaging system lies in that it can produce high resolution images of large area under all-weather condition. Therefore, it is widely applied to numerous fields such as high quality mapping, earth surface surveillance, search and rescue, mineral resources detection, automatic target recognition, and etc.
One of the main problems with SAR imagery is that the images generated are inevitably disturbed by multiplicative speckle noise. This is due to coherence of backscattered electromagnetic waves which produce the image data. Speckle noise in SAR image blankets image details and deteriorates image qualities, and may seriously impair the effects of automatic scene segmentation and target recognition. Since the cause of speckles is very special, general denoising approaches employed in digital image processing are not very applicable. Thus, reducing and suppressing speckles have always been a major concern of the SAR image community.
The requirements of denoising SAR image include not only filtering out noise but also preserving image details like edges and textures. Research scientists have already proposed several spatially adaptive filters which take advantage of the properties and features of speckle noise. Whereas, this thesis adopts a multiresolution point of view, applying wavelet transform, an extremely powerful mathematic tool, to denoising SAR image.
In this thesis, first there is a very brief introduction to synthetic aperture radar imaging principles. Then, the cause and statistical model of speckles in SAR image are analyzed. After that, a generalized description of wavelet transform and multiresolution analysis is presented. Based on these fundamentals, the probability distribution of wavelet coefficients of SAR image is investigated and then the classic spatially adaptive wavelet soft-thresholding scheme used for denoising natural image is employed to suppressing speckles. Furthermore, we propose a new approach to calculating the threshold and estimating related parameters according to local statistics of wavelet coefficients. Experiment results on actual SAR images show that the proposed method makes a good tradeoff between noise suppression and fine detail preservation. The denoised testing SAR images are superior to those processed by traditional spatial filters when they are subjected to both visual perception and numerical evaluation. At last, there is a short but insightful discussion of the significance of wavelet transform and multiresolution analysis to SAR image denoising.
合成孔径雷达成像的主要问题是生成的图像一般都会受到乘性斑点噪声的干扰。这是由于形成图像的背向散射电磁波相干造成的。SAR图像中的斑点噪声掩盖了图像细节,在视觉上降低了图像质量,并且会严重影响自动场景分割和目标识别的效果。由于SAR图像斑点噪声的成因比较特殊,一般的数字图像处理中所采用的降噪方法对SAR图像并不十分有效。所以,降低和抑制SAR图像的斑点噪声一直以来都是SAR图像研究的一个热点。
SAR图像降噪的要求,是在滤除噪声的同时,尽量保持原始图像的边缘和纹理等细节信息。科研人员根据SAR斑点噪声的性质和特点,已经提出了多种空间域自适应滤波器。而本文则是从多分辨率分析的角度出发,将小波变换这一强大的数学工具应用于SAR图像降噪。
本文首先简要介绍了合成孔径雷达成像原理,以及SAR图像的巨大作用。然后,简单地分析了SAR图像斑点噪声的形成原因和统计模型,接着大致描述了小波和多分辨率分析的基本原理。在这些背景知识的基础上,本文分析了SAR图像小波系数的分布特点,然后将经典的小波域自适应软阈值法应用于降低SAR图像斑点噪声。进一步,本文提出根据小波系数的局部统计量选取阈值以及估计相关参数的方法。对真实的SAR图像的实验结果表明,本文算法在降低噪声和保持边缘纹理细节之间取得了较好的平衡,处理后的SAR图像的视觉效果和质量评估参数都要优于传统的空间域滤波方法的处理结果。最后,本文深入分析了小波变换和多分辨率分析对于SAR图像降噪的意义,提出了将来可进一步深入研究的方向。
Synthetic aperture radar (SAR) imaging system was invented in the 50s and 60s of 20th century. One of the most important features of SAR imaging system lies in that it can produce high resolution images of large area under all-weather condition. Therefore, it is widely applied to numerous fields such as high quality mapping, earth surface surveillance, search and rescue, mineral resources detection, automatic target recognition, and etc.
One of the main problems with SAR imagery is that the images generated are inevitably disturbed by multiplicative speckle noise. This is due to coherence of backscattered electromagnetic waves which produce the image data. Speckle noise in SAR image blankets image details and deteriorates image qualities, and may seriously impair the effects of automatic scene segmentation and target recognition. Since the cause of speckles is very special, general denoising approaches employed in digital image processing are not very applicable. Thus, reducing and suppressing speckles have always been a major concern of the SAR image community.
The requirements of denoising SAR image include not only filtering out noise but also preserving image details like edges and textures. Research scientists have already proposed several spatially adaptive filters which take advantage of the properties and features of speckle noise. Whereas, this thesis adopts a multiresolution point of view, applying wavelet transform, an extremely powerful mathematic tool, to denoising SAR image.
In this thesis, first there is a very brief introduction to synthetic aperture radar imaging principles. Then, the cause and statistical model of speckles in SAR image are analyzed. After that, a generalized description of wavelet transform and multiresolution analysis is presented. Based on these fundamentals, the probability distribution of wavelet coefficients of SAR image is investigated and then the classic spatially adaptive wavelet soft-thresholding scheme used for denoising natural image is employed to suppressing speckles. Furthermore, we propose a new approach to calculating the threshold and estimating related parameters according to local statistics of wavelet coefficients. Experiment results on actual SAR images show that the proposed method makes a good tradeoff between noise suppression and fine detail preservation. The denoised testing SAR images are superior to those processed by traditional spatial filters when they are subjected to both visual perception and numerical evaluation. At last, there is a short but insightful discussion of the significance of wavelet transform and multiresolution analysis to SAR image denoising.
引文
[1]皮亦鸣,杨建宇,付毓生,杨晓波主编.合成孔径雷达成像原理.成都:电子科技大学出版社. 2007: 2-15.
[2] Maitre, H.著,孙洪译.合成孔径雷达图像处理.北京:电子工业出版社. 2005: 67-69.
[3] Goodman, J. Some fundamental properties of speckle. Journal of Optical Society of America. Nov. 1976, Vol. 66: 1145-1150.
[4]匡纲要,高贵,蒋咏梅.合成孔径雷达目标检测理论、算法及应用.湖南长沙:国防科技大学出版社. 2007: 45-47.
[5] Lee, J. Speckle suppression and analysis for synthetic aperture radar. Optical Engineering. May. 1986. Vol. 25: 636-643.
[6] Lee, J. Refined filtering of image noise using local statistics, Computer Graphics and Image Processing, Vol. 15, pp. 380-398, 1981.
[7] Kuan, D., Sawchuk, A., Strand, T., and Chavel, P. Adaptive restoration of images with speckle. IEEE Transactions on Acoustic Speech Signal Processing. Mar. 1987. Vol. 35: 373-383.
[8] Frost, V., Stiles, J., Shanmugan, K., and Holtzman, J. A model for radar images and its application to adaptive digital filtering of multiplicative noise. IEEE Transactions on Pattern Ana1ysis and Machine Intelligence. Feb. 1982. Vol. 2: 157-166.
[9] Baraldi, A. and Parmigiani, F. A refined gamma MAP SAR speckle filter with improved geometrical adaptivity. IEEE Transactions on Geoscience and Remote Sensing. Sep. 1995. Vol. 33: 1245-1257.
[10]张朝晖,潘春洪,马颂德.一种基于修正Frost核的SAR图像斑点噪声抑制方法.中国图象图形学报. 2005年4月.
[11] Burrus, C. S., Ramesh, A. G. and Guo, H. An Introduction to Wavelets and Wavelet Transforms: A Primer.(影印版)北京:机械工业出版社. 1997: 10-23.
[12] Gonzalez, R. C. and Woods, R. E. Digital Image Processing, Second Edition.(影印版)北京:电子工业出版社. 2004: 349-386.
[13] Donono, D. and Johnstone, I. Ideal spatial adaptation via wavelet shrinkage. Biometrika. 1994. Vol.81: 425-455.
[14] Donono, D. Denoising by soft-thresholding. IEEE Transactions on Information Theory. May. 1995. Vol. 41: 613-627.
[15] Guo, H., Udegard, J., Lung, M., Gopinath, R., Selesnick, I. and Burrus, C. Wavelet based speckle reduction with application to SAR based ATD/R. IEEE Proceedings of 1st International Conference on Image Processing. Nov. 1994. Vol. 1: 75-79.
[16]郭小卫,田铮.基于小波域边缘方向特征的SAR图象噪声抑制方法.中国图象图形学报. 2003年4月.
[17]武昕伟,朱兆达,张弓,郭春生.一种基于小波域隐马尔可夫模型的SAR相干斑抑制算法.中国图象图形学报. 2004年4月。
[18]周伟华,王鑫,罗斌,基于双树复小波变换的相位保持SAR图像降噪,中国图象图形学报,2007年5月。
[19] Achim, A., Tsakalides, P. and Bezerianos, A. SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling. IEEE Transactions on Geoscience and Remote Sensing. Aug. 2003. Vol. 41: 1773–1784,
[20] Solbo, S. and Eltoft, T.Г-WMAP: A statistical speckle filter operating in the wavelet domain. International Journal of Remote Sensing. Mar. 2004. Vol. 25, No. 5: 1019-1036.
[21] Solbo, S. and Eltoft, T. Homomorphic wavelet-based statistical despeckling of SAR images. IEEE Transactions on Geoscience and Remote Sensing. Apr. 2004. Vol. 42, No. 4: 711–721.
[22] Oliver, C. and Quegan, S. Understanding Synthetic Aperture Radar Images. SciTech Publishing. 1998.
[23] Gagnon, L. and Jouan, A. Speckle filtering of SAR images-a comparative study between complex-wavelet based and standard filters. Proceedings of SPIE Conference on Wavelet Applications in Signal and Image Processing. 1997. Vol. 3169: 81-91.
[24] Vidakovic, B. Statistical Modeling by Wavelets. New York: Wiley. 1999.
[25] Arsenault, H. and April, G. Properties of speckle integrated with a finite aperture and logarithmically transformed. Journal of Optical Society of America. Nov. 1976. Vol. 66, No. 11: 1160–1163.
[26] Xie, H., Pierce, L. and Ulaby, F. Statistical properties of logarithmically transformed speckle. IEEE Transactions on Geoscience and Remote Sensing. Mar. 2002. Vol. 40: 721–727.
[27] Chang, S. G., Yu, B. and Vetterli, M. Spatially adaptive thresholding with context modeling for image denoising. IEEE Transactions On Image Processing. Sep. 2000. Vol. 9, No. 9:1522-1531.
[28] Chang, S. G., Yu, B. and Vetterli, M. Adaptive wavelet thresholding with for image denoising and compression. IEEE Transactions On Image Processing. Sep. 2000. Vol. 9, No. 9: 1532-1546.
[29] Yuan, X. and Buckles, B. Subband noise estimation for adaptive wavelet shrinkage. Proceedings of the 17th International Conference on Pattern Recognition. 2004.
[30] Mallat, S. A Wavelet Tour of Signal Processing, Second Edition.(影印版)北京:机械工业出版社. 2003: 153-156.
[31]贾承丽,匡纲要. SAR图像去斑方法.中国图象图形学报. 2005年2月.
[32] Mallat, S. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence. Jul. 1989. Vol. 11: 674–693.
[33] Foucher, S. Benie, G. and Boucher, J. Multiscale MAP filtering of SAR images. IEEE Transactions on Image Processing. Jan. 2001. Vol. 10, No. 1: 49-60.
[2] Maitre, H.著,孙洪译.合成孔径雷达图像处理.北京:电子工业出版社. 2005: 67-69.
[3] Goodman, J. Some fundamental properties of speckle. Journal of Optical Society of America. Nov. 1976, Vol. 66: 1145-1150.
[4]匡纲要,高贵,蒋咏梅.合成孔径雷达目标检测理论、算法及应用.湖南长沙:国防科技大学出版社. 2007: 45-47.
[5] Lee, J. Speckle suppression and analysis for synthetic aperture radar. Optical Engineering. May. 1986. Vol. 25: 636-643.
[6] Lee, J. Refined filtering of image noise using local statistics, Computer Graphics and Image Processing, Vol. 15, pp. 380-398, 1981.
[7] Kuan, D., Sawchuk, A., Strand, T., and Chavel, P. Adaptive restoration of images with speckle. IEEE Transactions on Acoustic Speech Signal Processing. Mar. 1987. Vol. 35: 373-383.
[8] Frost, V., Stiles, J., Shanmugan, K., and Holtzman, J. A model for radar images and its application to adaptive digital filtering of multiplicative noise. IEEE Transactions on Pattern Ana1ysis and Machine Intelligence. Feb. 1982. Vol. 2: 157-166.
[9] Baraldi, A. and Parmigiani, F. A refined gamma MAP SAR speckle filter with improved geometrical adaptivity. IEEE Transactions on Geoscience and Remote Sensing. Sep. 1995. Vol. 33: 1245-1257.
[10]张朝晖,潘春洪,马颂德.一种基于修正Frost核的SAR图像斑点噪声抑制方法.中国图象图形学报. 2005年4月.
[11] Burrus, C. S., Ramesh, A. G. and Guo, H. An Introduction to Wavelets and Wavelet Transforms: A Primer.(影印版)北京:机械工业出版社. 1997: 10-23.
[12] Gonzalez, R. C. and Woods, R. E. Digital Image Processing, Second Edition.(影印版)北京:电子工业出版社. 2004: 349-386.
[13] Donono, D. and Johnstone, I. Ideal spatial adaptation via wavelet shrinkage. Biometrika. 1994. Vol.81: 425-455.
[14] Donono, D. Denoising by soft-thresholding. IEEE Transactions on Information Theory. May. 1995. Vol. 41: 613-627.
[15] Guo, H., Udegard, J., Lung, M., Gopinath, R., Selesnick, I. and Burrus, C. Wavelet based speckle reduction with application to SAR based ATD/R. IEEE Proceedings of 1st International Conference on Image Processing. Nov. 1994. Vol. 1: 75-79.
[16]郭小卫,田铮.基于小波域边缘方向特征的SAR图象噪声抑制方法.中国图象图形学报. 2003年4月.
[17]武昕伟,朱兆达,张弓,郭春生.一种基于小波域隐马尔可夫模型的SAR相干斑抑制算法.中国图象图形学报. 2004年4月。
[18]周伟华,王鑫,罗斌,基于双树复小波变换的相位保持SAR图像降噪,中国图象图形学报,2007年5月。
[19] Achim, A., Tsakalides, P. and Bezerianos, A. SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling. IEEE Transactions on Geoscience and Remote Sensing. Aug. 2003. Vol. 41: 1773–1784,
[20] Solbo, S. and Eltoft, T.Г-WMAP: A statistical speckle filter operating in the wavelet domain. International Journal of Remote Sensing. Mar. 2004. Vol. 25, No. 5: 1019-1036.
[21] Solbo, S. and Eltoft, T. Homomorphic wavelet-based statistical despeckling of SAR images. IEEE Transactions on Geoscience and Remote Sensing. Apr. 2004. Vol. 42, No. 4: 711–721.
[22] Oliver, C. and Quegan, S. Understanding Synthetic Aperture Radar Images. SciTech Publishing. 1998.
[23] Gagnon, L. and Jouan, A. Speckle filtering of SAR images-a comparative study between complex-wavelet based and standard filters. Proceedings of SPIE Conference on Wavelet Applications in Signal and Image Processing. 1997. Vol. 3169: 81-91.
[24] Vidakovic, B. Statistical Modeling by Wavelets. New York: Wiley. 1999.
[25] Arsenault, H. and April, G. Properties of speckle integrated with a finite aperture and logarithmically transformed. Journal of Optical Society of America. Nov. 1976. Vol. 66, No. 11: 1160–1163.
[26] Xie, H., Pierce, L. and Ulaby, F. Statistical properties of logarithmically transformed speckle. IEEE Transactions on Geoscience and Remote Sensing. Mar. 2002. Vol. 40: 721–727.
[27] Chang, S. G., Yu, B. and Vetterli, M. Spatially adaptive thresholding with context modeling for image denoising. IEEE Transactions On Image Processing. Sep. 2000. Vol. 9, No. 9:1522-1531.
[28] Chang, S. G., Yu, B. and Vetterli, M. Adaptive wavelet thresholding with for image denoising and compression. IEEE Transactions On Image Processing. Sep. 2000. Vol. 9, No. 9: 1532-1546.
[29] Yuan, X. and Buckles, B. Subband noise estimation for adaptive wavelet shrinkage. Proceedings of the 17th International Conference on Pattern Recognition. 2004.
[30] Mallat, S. A Wavelet Tour of Signal Processing, Second Edition.(影印版)北京:机械工业出版社. 2003: 153-156.
[31]贾承丽,匡纲要. SAR图像去斑方法.中国图象图形学报. 2005年2月.
[32] Mallat, S. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence. Jul. 1989. Vol. 11: 674–693.
[33] Foucher, S. Benie, G. and Boucher, J. Multiscale MAP filtering of SAR images. IEEE Transactions on Image Processing. Jan. 2001. Vol. 10, No. 1: 49-60.