基于Curvelet变换的SAR图像相干斑抑制
摘要
随着合成孔径雷达(Synthetic Aperture Radar, SAR)的发展,其应用越来越广泛,但是由于SAR图像在成像时,其散射回波具有相干作用,使得SAR图像具有相干斑噪声,并被定义为“乘性”噪声。这种相干斑噪声严重影响了SAR图像的质量,降低了其空间分辨率,因此,为了有效的理解和解译SAR图像,必须对其进行相干斑抑制,同时要有效的保持图像的边缘等细节信息。然而由于SAR图像成像时地物目标的复杂性,使得SAR图像不具有明确的模型,传统的图像去噪方法难以有效的抑制SAR图像的相干斑噪声,而多尺度几何分析的出现,为SAR图像的相干斑抑制提供了方法。
本文利用多尺度几何分析工具——Curvelet,它具有尺度、空间位置和尺度三个参数,使得它有很强的方向性和和各向异性,能够最优的稀疏表示具有曲线和直线边缘的目标。根据这些特性,论文主要进行了以下三个方面的工作。
1)分析了SAR图像进行Curvelet变换后的系数统计特性,利用两个零均值的混合高斯函数对每一层的系数进行拟合,在此基础上用贝叶斯收缩因子对系数进行收缩,重构图像后,用均值滤波和非线性各向异性扩散方法克服了Curvelet本身不足带来的划痕效应以及点目标丢失的缺点。
2)针对Curvelet系数在各个子带中系数的聚集特性,设计了一个基于局部特性的系数收缩因子。由于Curvelet不能有效的处理图像中的点目标,引入了具有一维奇异性的平稳小波,利用小波层间系数的相关性,有效的处理了边缘上的点目标,最后利用差值缩减的方法得到图像中的点目标。
3)改善了Starck等人提出的Curvelet域硬阈值方法对Curvelet系数的不连续处理,设计了一个连续的阈值函数,并且通过对最高层Curvelet系数的两次不同处理,两次重构的方法有效的保持了图像的弱纹理信息,并利用复扩散的方法对图像进行了均值补偿。
实验结果表明,以上方法均能在有效抑制SAR图像斑点噪声的同时,也能有效的保持图像的边缘等细节信息。
With the development of the Synthetic Aperture Radar(SAR), it’s widely used in many domains, however, the SAR images contain speckle because of the coherence effects between the backscattered signals when imaging, the speckle noise can typically be modeled as multiplicative. The speckle reduces the image quality and the spatial resolution of SAR image. In order to understand and interpret the SAR image, it’s necessary to despeckle but keep the details at the same time. The complexity of the scatter targets make the SAR image doesn’t have an accurate model, so the traditional denoising methods don’t work effectively when despeckle. However, the appearance of multiscale geometric analysis provides a new way to despeckle effectively.
In this paper, one of the multiscale geometric analysis tools, curvelet is used to despeckle the SAR image. Curvelet is a multiscale transform with frame elements indexed by scale, location and orientation parameters, the frames can represent edges and other singularities along curves efficiently. Based on this, three new despeckling methods are proposed, the main innovative points are as follows:
1) The statistical characteristics of curvelet coefficients of the SAR image is analyzed first, then a mixture density of two zero-mean Gaussian functions is proposed to fit the actual histogram of the coefficients of every subband. Based on this, a Bayesian shrink factor is derived to shrink the curvelet coefficient, lastly, the mean filter and the nonlinear anisotropic diffusion are used to deal with the reconstructed image to overcome the shortcomings of curvelet.
2) Contraposing the aggregation property of the curvelet coefficients in every subband, a shrink factor is proposed. The stationary wavelet is introduced to deal with the point targets because the curvelet doesn’t work well on it, in the wavelet domain, the pertinence of the wavelet coefficients is used, so the point targets on the edges are well maintained, at last, the shrink of the difference image between the original image and the result image of wavelet is used to get the point targets.
3) A continuous threshold function is proposed to improve the hard-thresholding function proposed by Stark in the curvelet domain. In the curvelet domain, the coefficients in the finest subband are dealt with using different principles twice, and reconstruct the image twice so as to keep the weak texture well, and the complex diffusion is used to compensate the mean value. Experimental results demonstrate that the three methods can despeckle the SAR image effectively, and keep the details well at the same time.
本文利用多尺度几何分析工具——Curvelet,它具有尺度、空间位置和尺度三个参数,使得它有很强的方向性和和各向异性,能够最优的稀疏表示具有曲线和直线边缘的目标。根据这些特性,论文主要进行了以下三个方面的工作。
1)分析了SAR图像进行Curvelet变换后的系数统计特性,利用两个零均值的混合高斯函数对每一层的系数进行拟合,在此基础上用贝叶斯收缩因子对系数进行收缩,重构图像后,用均值滤波和非线性各向异性扩散方法克服了Curvelet本身不足带来的划痕效应以及点目标丢失的缺点。
2)针对Curvelet系数在各个子带中系数的聚集特性,设计了一个基于局部特性的系数收缩因子。由于Curvelet不能有效的处理图像中的点目标,引入了具有一维奇异性的平稳小波,利用小波层间系数的相关性,有效的处理了边缘上的点目标,最后利用差值缩减的方法得到图像中的点目标。
3)改善了Starck等人提出的Curvelet域硬阈值方法对Curvelet系数的不连续处理,设计了一个连续的阈值函数,并且通过对最高层Curvelet系数的两次不同处理,两次重构的方法有效的保持了图像的弱纹理信息,并利用复扩散的方法对图像进行了均值补偿。
实验结果表明,以上方法均能在有效抑制SAR图像斑点噪声的同时,也能有效的保持图像的边缘等细节信息。
With the development of the Synthetic Aperture Radar(SAR), it’s widely used in many domains, however, the SAR images contain speckle because of the coherence effects between the backscattered signals when imaging, the speckle noise can typically be modeled as multiplicative. The speckle reduces the image quality and the spatial resolution of SAR image. In order to understand and interpret the SAR image, it’s necessary to despeckle but keep the details at the same time. The complexity of the scatter targets make the SAR image doesn’t have an accurate model, so the traditional denoising methods don’t work effectively when despeckle. However, the appearance of multiscale geometric analysis provides a new way to despeckle effectively.
In this paper, one of the multiscale geometric analysis tools, curvelet is used to despeckle the SAR image. Curvelet is a multiscale transform with frame elements indexed by scale, location and orientation parameters, the frames can represent edges and other singularities along curves efficiently. Based on this, three new despeckling methods are proposed, the main innovative points are as follows:
1) The statistical characteristics of curvelet coefficients of the SAR image is analyzed first, then a mixture density of two zero-mean Gaussian functions is proposed to fit the actual histogram of the coefficients of every subband. Based on this, a Bayesian shrink factor is derived to shrink the curvelet coefficient, lastly, the mean filter and the nonlinear anisotropic diffusion are used to deal with the reconstructed image to overcome the shortcomings of curvelet.
2) Contraposing the aggregation property of the curvelet coefficients in every subband, a shrink factor is proposed. The stationary wavelet is introduced to deal with the point targets because the curvelet doesn’t work well on it, in the wavelet domain, the pertinence of the wavelet coefficients is used, so the point targets on the edges are well maintained, at last, the shrink of the difference image between the original image and the result image of wavelet is used to get the point targets.
3) A continuous threshold function is proposed to improve the hard-thresholding function proposed by Stark in the curvelet domain. In the curvelet domain, the coefficients in the finest subband are dealt with using different principles twice, and reconstruct the image twice so as to keep the weak texture well, and the complex diffusion is used to compensate the mean value. Experimental results demonstrate that the three methods can despeckle the SAR image effectively, and keep the details well at the same time.
引文
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[5] Brenner A. R. and Roessing L. Radar Imaging of Urban Areas by Means of Very High-Resolution SAR and Interferometric SAR. IEEE Transactions on Geoscience and Remote Sensing. 2008. 46(10). P2971-2982.
[6] Yijun He, Perrie W., Tao Xie, et al. Ocean wave spectra from a linear Polarimetric SAR. IEEE Transactions on Geoscience and Remote Sensing. 2004. 42(11). P2623-2631.
[7] Moser G.. and Karl W. C. Unsupervised Change Detection From Multichannel SAR Data by Markovian Data Fusion. IEEE Transactions on Geoscience and Remote Sensing. 2009. 47(7). P2114-2128.
[8] Margarit G.., Mallorqui J. J., Rius J.M, et al. On the Usage of GRECOSAR, an Orbital Polarimetric SAR Simulator of Complex Targets, to Vessel Classification Studies. IEEE Transactions on Geoscience and Remote Sensing. 2006. 44(12). P3517-3526.
[9] Gamba P., Dell Acqua F. and Lisini G. Change Detection of Multitemporal SAR Data in Urban Areas Combining Feature-Based and Pixel-Based Techniques. IEEE Transactions on Geoscience and Remote Sensing. 2006. 44(10). P2820-2827.
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[11] Lance M. Kaplan. Analysis of Multiplicative Speckle Models for Template-Based SAR ATR. 2001. 37(4). P1424-1432.
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[13]冈萨雷斯等著,阮秋琦等译.数字图像处理.第二版.北京:电子工业出版社,2003.
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[25] A. Piurica, W. Philips, I. Lemahieu, et al. A joint inter- and intrascale statisticalmodel for Bayesian wavelet based image denoising. IEEE Transaction on Image Processing. 2002. 11(5). P545-557.
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[27] N. Xie, L. E. Pierce and F. T. Ulaby. SAR speckle reduction using wavelet denoising and Markov random field modeling. IEEE Transactions on Geoscience and Remote Sensing. 2002. 40(10). P2196-2212.
[28] Duan Gleich and Mihai Datcu. Wavelet-Based Despeckling of SAR Images Using Gauss-Markov Random Fields. IEEE Transactions on Geoscience and Remote Sensing. 2007. 45(12). P4127-4143.
[29] A. Grossman and J. Morlet. Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape. SIAM J. Appl. 1984. 15. P723-737.
[30] C. K. Chui. An Introduction to Wavelets. San Diego: Academic Press. 1992.
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[33] Beylkin G. Discrete Radon Transform. IEEE Trans ASSP. 1987. 35(1). P162-172.
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[36] Emmanuel J. Candes and David L. Donoho. New Tight Frames of Curvelets and Optimal Representations of Objects with Singularities. Commun Pure Appl. 2004. 57(2). P219-266. C2
[37] S. G. Chang and M. Vetterli. Spatial adaptive wavelet thresholding for image denoising. IEEE Int. Symp. Image Processing. 1997.
[38] A. Dempster, N. Laird, D. Rubin. Maximum likelihood estimation from incomplete data via EM algorithm. J. Royal Statistical Society Series B. 1977. 39. P1-38.
[39] WANG Ping-bo, CAI Zhi-ming, LIU Wang-suo. EM estimation of PDF parameters for Gassian mixture processes. Technical Acoustics, 2007. 26(3). P498-502.
[40] Arsenault H H, April G. Properties of speckle integrated with a finite aperture and logarithmically transformed. Journal of the optical society of America. 1976. 66. P1160-1163.
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[42] F. Argnti and L. Alparone. Speckle removal from SAR images in the undecimated wavelet domain. IEEE Transactions on Geoscience and Remote Sensing. 2002. 40. P2363-2374.
[43] S. Foucher, G. B. Benie and J. M. Boucher. Multiscale MAP filtering of SAR images. IEEE Transaction on Image Processing. 2001. 10. P49-60.
[44] H. Xie L. E. Pierce and F. T. Ulaby. Statistical properties of logarithmically transformed speckle. IEEE Transactions on Geoscience and Remote Sensing. 2002. 40. P721-727.
[45] R. Touzi, A. Lopes and P. Bousquet. A statistical and geometrical edge detector for SAR images. IEEE Transactions on Geoscience and Remote Sensing. 1988. 26. P764-773.
[46] MA Jian-wei, Gerlind Plonka. Combined Curvelet Shrinkage and Nonlinear Anisotropic Diffusion. IEEE Transactions on Image Processing, 2007. 16(9). P2198-2206.
[47] J. Weickert. Anisotropic Diffusion in Image Processing. Teubner, Stuttgart. 1998.
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[56] Guy Gilboa, Nir Sochen and Yehoshua Y Zeevi. Image Enhancement and Denoising by Complex Diffusion Processes. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2003. 26(8). P1020-1036.
[2] A. Freeman, D. Evans, J. J. VanZyl. SAR Applications in the 21st Century. European Conference on Synthetic Aperture Radar, Germany, 1996. P25-30.
[3] J. B. Boisvert, T. J. Pultz, R. J. Brown, et al. Potential of Synthetic Aperture Radar for Large-Scale Soil Moisture Monitoring: A Review. Canadian Journal of Remote Sensing. 1995. 22(1). P2-13.
[4] Y. Grevier, T. J. Pultz, T. I. Lukowski, et al. Temporal Analysis of ERS-1 SAR Backscatter for Hydrology Applications. Canadian Journal of Remote Sensing. 1995. 22(1). P65-76.
[5] Brenner A. R. and Roessing L. Radar Imaging of Urban Areas by Means of Very High-Resolution SAR and Interferometric SAR. IEEE Transactions on Geoscience and Remote Sensing. 2008. 46(10). P2971-2982.
[6] Yijun He, Perrie W., Tao Xie, et al. Ocean wave spectra from a linear Polarimetric SAR. IEEE Transactions on Geoscience and Remote Sensing. 2004. 42(11). P2623-2631.
[7] Moser G.. and Karl W. C. Unsupervised Change Detection From Multichannel SAR Data by Markovian Data Fusion. IEEE Transactions on Geoscience and Remote Sensing. 2009. 47(7). P2114-2128.
[8] Margarit G.., Mallorqui J. J., Rius J.M, et al. On the Usage of GRECOSAR, an Orbital Polarimetric SAR Simulator of Complex Targets, to Vessel Classification Studies. IEEE Transactions on Geoscience and Remote Sensing. 2006. 44(12). P3517-3526.
[9] Gamba P., Dell Acqua F. and Lisini G. Change Detection of Multitemporal SAR Data in Urban Areas Combining Feature-Based and Pixel-Based Techniques. IEEE Transactions on Geoscience and Remote Sensing. 2006. 44(10). P2820-2827.
[10] Chris Oliver and Shaun Quegan. Understanding Synthetic Aperture Radar Images. Boston, MA: Artech House Publishers. 1998. P96-99.
[11] Lance M. Kaplan. Analysis of Multiplicative Speckle Models for Template-Based SAR ATR. 2001. 37(4). P1424-1432.
[12] M. Tur, K. C. Chin, and J. W. Goodman. When is speckle noise multiplicative. Applied Optics. 1982, 21(7). P1157-1159.
[13]冈萨雷斯等著,阮秋琦等译.数字图像处理.第二版.北京:电子工业出版社,2003.
[14] Lopes A, Nezry E, Touzi R, et al. Maximum a posteriori speckle filtering and first order texture models in SAR images. Proceedings of IGARSS, 1990. P2409-2412.
[15] Baraldi A, Parmigiani F. A refined Gamma MAP SAR speckle filter with improved geometrical adaptivity. IEEE Transactions on Geoscience and Remote Sensing, 1995. 33(5). P1245-1257.
[16] Lee J S. Digital image enhancement and noise filtering by use of local statistics. IEEE Transactions on Pattern Analysis Machine Intelligence. 1980. PAMI-2. P165-168.
[17] Lee J S. Refined filtering of image noise using local statistics. Computer Graphics and Image Processing. 1981. 15(3). P380-389.
[18] V. S. Frost, J. A. Stiles, K. S. Shanmugan, et al. A model for radar images and its application to adaptive digital filtering of multiplicative noise. IEEE Transactions on Pattern Analysis Machine Intelligence. 1982. PAMI-4. P157-166.
[19] D. T. Kuan, A. A. Sawchuk, T. C. Strand, et al. Adaptive noise smoothing filter for images with signal-dependent noise. IEEE Transactions on Pattern Analysis Machine Intelligence. 1985. PAMI-2. P165-177.
[20] David L. Donoho. De-noising by Soft-Thresholding. IEEE Transactions on Information Theory. 1995. 41(3). P613-627.
[21] M. Walessa and M. Datcu. Model-based despeckling and information extraction from SAR images. IEEE Transactions on Geoscience and Remote Sensing. 2000. 38(5). P2258-2269.
[22] M. Dai, C. Peng, A. K. Chan, et al. Bayesian wavelet shrinkage with edge detection for SAR image despeckling. IEEE Transactions on Geoscience and Remote Sensing. 2004. 42(8). P1642-4648.
[23] M. Malfait and D. Roose. Wavelet-based image denoising using a Markov random fields a prior model. IEEE Transaction on Image Processing. 1997. 6(4). P549-565.
[24] J. Portilla, V. Strela and M. J. Wainwright, et al. Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Transaction on Image Processing. 2003. 12(11). P1338-1351.
[25] A. Piurica, W. Philips, I. Lemahieu, et al. A joint inter- and intrascale statisticalmodel for Bayesian wavelet based image denoising. IEEE Transaction on Image Processing. 2002. 11(5). P545-557.
[26] A. Achim, P. Tsakalides and A. Bezerianos. SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling. IEEE Transactions on Geoscience and Remote Sensing. 2003. 41(8). P1773-1784.
[27] N. Xie, L. E. Pierce and F. T. Ulaby. SAR speckle reduction using wavelet denoising and Markov random field modeling. IEEE Transactions on Geoscience and Remote Sensing. 2002. 40(10). P2196-2212.
[28] Duan Gleich and Mihai Datcu. Wavelet-Based Despeckling of SAR Images Using Gauss-Markov Random Fields. IEEE Transactions on Geoscience and Remote Sensing. 2007. 45(12). P4127-4143.
[29] A. Grossman and J. Morlet. Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape. SIAM J. Appl. 1984. 15. P723-737.
[30] C. K. Chui. An Introduction to Wavelets. San Diego: Academic Press. 1992.
[31] E. J. Candes. Ridgelets: Theory and Applications. PH. D. Thesis, Department of Statistics, Stanford University, 1999.
[32] E. J. Candes. Harmonic analysis of neural networks. Applied and Computational Harmonic Analysis. 1999. 6. P197-218.
[33] Beylkin G. Discrete Radon Transform. IEEE Trans ASSP. 1987. 35(1). P162-172.
[34] David L. Donoho and Mark R. Duncan. Digital Curvelet Transform: Strategy, Implementation and Experiments. SPIE proceedings series. 1999. P12-29.
[35] E . J. Candes, L. Demanet, D. L. Donoho, et al. Fast Discrete Curvelet Transforms. Applied and Computational Mathematics, Caltech, Pasadena, 2005. CA 91125. P1-43.
[36] Emmanuel J. Candes and David L. Donoho. New Tight Frames of Curvelets and Optimal Representations of Objects with Singularities. Commun Pure Appl. 2004. 57(2). P219-266. C2
[37] S. G. Chang and M. Vetterli. Spatial adaptive wavelet thresholding for image denoising. IEEE Int. Symp. Image Processing. 1997.
[38] A. Dempster, N. Laird, D. Rubin. Maximum likelihood estimation from incomplete data via EM algorithm. J. Royal Statistical Society Series B. 1977. 39. P1-38.
[39] WANG Ping-bo, CAI Zhi-ming, LIU Wang-suo. EM estimation of PDF parameters for Gassian mixture processes. Technical Acoustics, 2007. 26(3). P498-502.
[40] Arsenault H H, April G. Properties of speckle integrated with a finite aperture and logarithmically transformed. Journal of the optical society of America. 1976. 66. P1160-1163.
[41] S. Fukuda and H. Hirosawa. Suppression of speckle in synthetic aperture radar images using wavelet. International Journal of Remote Sensing. 1998. 19(3). P507-519.
[42] F. Argnti and L. Alparone. Speckle removal from SAR images in the undecimated wavelet domain. IEEE Transactions on Geoscience and Remote Sensing. 2002. 40. P2363-2374.
[43] S. Foucher, G. B. Benie and J. M. Boucher. Multiscale MAP filtering of SAR images. IEEE Transaction on Image Processing. 2001. 10. P49-60.
[44] H. Xie L. E. Pierce and F. T. Ulaby. Statistical properties of logarithmically transformed speckle. IEEE Transactions on Geoscience and Remote Sensing. 2002. 40. P721-727.
[45] R. Touzi, A. Lopes and P. Bousquet. A statistical and geometrical edge detector for SAR images. IEEE Transactions on Geoscience and Remote Sensing. 1988. 26. P764-773.
[46] MA Jian-wei, Gerlind Plonka. Combined Curvelet Shrinkage and Nonlinear Anisotropic Diffusion. IEEE Transactions on Image Processing, 2007. 16(9). P2198-2206.
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