基于小波理论的SAR图像压缩方法研究
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摘要
合成孔径雷达(SAR)利用合成天线孔径技术可以产生更高空间分辨率的雷达图像。雷达系统可以获取大量的数据，然而随着数据采集量的增加，其传输和存储能力变得相对较弱。而且，尽管随着科技的发展媒体的存储密度正在逐步提高，但是新数据的生成能力增加更强。有多种方法可以降低数据率，可也会同时使系统整体运行效果降低。例如，除非用更长的相位天线，脉冲重复频率的降低会增加相位模糊，相位分辨率降低。同时，减小距离分辨率也会降低系统带宽。仅仅简单的降低量化比特数会增加数字化噪声，因而损坏脉冲响应函数、图像动态范围和辐射精确性。所以，高效的数据压缩算法就成了发展先进SAR系统的一个重要方向。
SAR图像的几个特点影响图像压缩算法的设计。首先是斑点噪声现象，一个发展成熟的斑点是随机的，无序的，严重降低SAR图像质量；第二是SAR图像上既有细节纹理信息又有大量均匀区域，这样就有必要考虑减少均匀区域的编码比特数；第三是不像其他如光学传感器图像数据那样，SAR图像数据的动态范围很高。这种差异就意味着是用于光学数据的编解码算法对SAR数据并不一定是最优的，甚至可能根本不合适。
近年来迅速发展的小波变换理论的优越性在于它除了具有传统的Fourier变换的优点外，还较好的解决了Fourier变换在时域和频域的矛盾，能够在时域和频域上同时具有很好的局部化特性。而且小波变换还具有时间—频率定位能力，并初步实现了图像中平稳成分和非平稳成分的分离。低频成分精确定位于频率域，且基本上是平稳的，高频成分精确定位于空间域，且为非平稳的。处理非平稳信号是统计信号处理的一个难点，但对于图像，其非平稳成分通常表现为边缘、纹理等等。这些非平稳成分被小波变换精确定位以后有可能实现图像的高效编码。
本文在对SAR图像数据的信息特征进行了详细阐述的基础上，利用小波理论分析近年来比较流行嵌入式压缩编码方法，来研究适用于SAR图像的压缩方法，取得以下研究成果：
(1)考虑到SAR图像的动态范围比较大，而且SAR图像斑点噪声模型大部分是乘性噪声，先对其进行对数变换，既可以缩小数据的动态范围，也可以把
乘性噪声转变成加性噪声模型。对数变换之后再进行小波变换。
(2)压缩过程开始之前在小波域内先进行去斑点处理，去斑点的滤波方法
采用的是基于纹理信息的自适应闽值处理。与未经去斑点处理的图像相比噪声明
显减少。
(3)在本文我们采用了能量检测准则来进行小波分解，对于任何纹理信息
丰富的子频带再进一步分解，得到异于塔形结构的树形结构小波分解图，可以对
分解层数较少的均匀区域用较少比特进行编码，而用较多比特来编码细尺度的细
节纹理信息，这样可以在同样的码率下提高压缩效果。
(4)采用嵌入式编码和渐进性传输的方法，用户可以根据需要在任何时候
停止比特码流传输，并能在任何位置以精确的码率和失真度来解压缩和重建图
像。
(5)根据SAR图像应用目的不同，可以有各种不同的评价标准。在文中我
们提出了均方误差、峰值信噪比、均值信噪比、同质区域的均值和标准偏差以及
视觉效果等各种准则。利用这些准则对传统的SPIHT压缩方法和本文的方法进
行比较，可以看出我们的算法在各方面都明显优于SPIHT算法。
Synthetic Aperture Radar(SAR),with "all weather",day or night imaging capabilities ,is an important role in the domination of Earth observation. Radar system has produced plenty of data for object imaging and terrain cartography. However, with the rapid increase of data collection ,the capability of transmission and storage of SAR is relatively infirm. Though memory density is gradually improving, the producing ability of new data is increasing more rapidly. There are many kinds of methods which can reduce data rate, while the whole running effect of the system is depressed. So high effect data compression algorithm is an important tool to achieve advanced SAR system.
SAR images have several characteristics which affact the design of image compression algorithm. The first is speckles: a mature speckle is stochastic and out-of-order, and severely depresses SAR images quality. The second is that SAR images have both detailed texture information and many uniform regions. It is necessary to reduce bit rate of uniform regions. The last is that high dynamic range of SAR image data which is not the same as optical image data. This kind of difference means that those encoding/decoding algorithm for optical image data is not optimal for SAR data, and even not equal.
The superiority of Wavelet transform is that it both has the merits of Fourier transform and settle the conflict of Fourier transform in time field and frequency field and can have good local speciality in both time field and frequency field. Wavelet transform also has time-frequency orienting ability and realize the abruption of the balanced and unbalanced component in images.
This paper, based on particularly expatiating information characters in SAR image data, will investigate compression algorithm applying for SAR images by analyzing embedded encoding algorithms using wavelet theory. Using several standards to evaluate our method and SPIHT algorithm, it is clear that our method outgoes SPIHT algorithm.
SAR图像的几个特点影响图像压缩算法的设计。首先是斑点噪声现象，一个发展成熟的斑点是随机的，无序的，严重降低SAR图像质量；第二是SAR图像上既有细节纹理信息又有大量均匀区域，这样就有必要考虑减少均匀区域的编码比特数；第三是不像其他如光学传感器图像数据那样，SAR图像数据的动态范围很高。这种差异就意味着是用于光学数据的编解码算法对SAR数据并不一定是最优的，甚至可能根本不合适。
近年来迅速发展的小波变换理论的优越性在于它除了具有传统的Fourier变换的优点外，还较好的解决了Fourier变换在时域和频域的矛盾，能够在时域和频域上同时具有很好的局部化特性。而且小波变换还具有时间—频率定位能力，并初步实现了图像中平稳成分和非平稳成分的分离。低频成分精确定位于频率域，且基本上是平稳的，高频成分精确定位于空间域，且为非平稳的。处理非平稳信号是统计信号处理的一个难点，但对于图像，其非平稳成分通常表现为边缘、纹理等等。这些非平稳成分被小波变换精确定位以后有可能实现图像的高效编码。
本文在对SAR图像数据的信息特征进行了详细阐述的基础上，利用小波理论分析近年来比较流行嵌入式压缩编码方法，来研究适用于SAR图像的压缩方法，取得以下研究成果：
(1)考虑到SAR图像的动态范围比较大，而且SAR图像斑点噪声模型大部分是乘性噪声，先对其进行对数变换，既可以缩小数据的动态范围，也可以把
乘性噪声转变成加性噪声模型。对数变换之后再进行小波变换。
(2)压缩过程开始之前在小波域内先进行去斑点处理，去斑点的滤波方法
采用的是基于纹理信息的自适应闽值处理。与未经去斑点处理的图像相比噪声明
显减少。
(3)在本文我们采用了能量检测准则来进行小波分解，对于任何纹理信息
丰富的子频带再进一步分解，得到异于塔形结构的树形结构小波分解图，可以对
分解层数较少的均匀区域用较少比特进行编码，而用较多比特来编码细尺度的细
节纹理信息，这样可以在同样的码率下提高压缩效果。
(4)采用嵌入式编码和渐进性传输的方法，用户可以根据需要在任何时候
停止比特码流传输，并能在任何位置以精确的码率和失真度来解压缩和重建图
像。
(5)根据SAR图像应用目的不同，可以有各种不同的评价标准。在文中我
们提出了均方误差、峰值信噪比、均值信噪比、同质区域的均值和标准偏差以及
视觉效果等各种准则。利用这些准则对传统的SPIHT压缩方法和本文的方法进
行比较，可以看出我们的算法在各方面都明显优于SPIHT算法。
Synthetic Aperture Radar(SAR),with "all weather",day or night imaging capabilities ,is an important role in the domination of Earth observation. Radar system has produced plenty of data for object imaging and terrain cartography. However, with the rapid increase of data collection ,the capability of transmission and storage of SAR is relatively infirm. Though memory density is gradually improving, the producing ability of new data is increasing more rapidly. There are many kinds of methods which can reduce data rate, while the whole running effect of the system is depressed. So high effect data compression algorithm is an important tool to achieve advanced SAR system.
SAR images have several characteristics which affact the design of image compression algorithm. The first is speckles: a mature speckle is stochastic and out-of-order, and severely depresses SAR images quality. The second is that SAR images have both detailed texture information and many uniform regions. It is necessary to reduce bit rate of uniform regions. The last is that high dynamic range of SAR image data which is not the same as optical image data. This kind of difference means that those encoding/decoding algorithm for optical image data is not optimal for SAR data, and even not equal.
The superiority of Wavelet transform is that it both has the merits of Fourier transform and settle the conflict of Fourier transform in time field and frequency field and can have good local speciality in both time field and frequency field. Wavelet transform also has time-frequency orienting ability and realize the abruption of the balanced and unbalanced component in images.
This paper, based on particularly expatiating information characters in SAR image data, will investigate compression algorithm applying for SAR images by analyzing embedded encoding algorithms using wavelet theory. Using several standards to evaluate our method and SPIHT algorithm, it is clear that our method outgoes SPIHT algorithm.
引文
[1] A.Singh, Conference record of the 27th asilomar conference on signals, Systems&Computers, IEEE Computer Society Press,November, Vol.2,1993
[2] A. Grossman and J. morlet, Decomposition for Hardy Function into Square Integrabal Wavelets of Constant Shape SLAM, J. Math., 1984, vol. 15:723-736
[3] W. R. Zettler, et al, Application of Compactly Supported Wavelets to Image Compression , SPIE, Vol. 1244 Image Recognition Algorithm and Techniques 1990, 150-160
[4] M. Antonini, et al , Image Coding using Wavelet Transform ,IEEE, Trans. Image Proc., 1992, 1(2) :205-220
[5] Shapiro J M. Embedded image coding using zerotree of wavelet coefficients. IEEE Trans. Signal Processing, 1993,41 (12) :3445-3462．
[6] Lurie, J.B,B.W.Evans,B.Ringer,M.Yeats, image quality measures to assess hyperspectral compression techniques, Proceedings of Conference on Microwave Instrumentation and Satellite Photogrammetry for Remote Sensing of the Earth ,SPIE Vol.2313,1994,pp.2-14
[7] Ulaby, F. T., R. K. Moore, and A. K. Fung, 1986; Tsang, L., J. A. Kong, and R. T. Shin,1985; Fung A. K. 1994; Kong, J. A. 1990; Kuga, Y, M. W. Whitt, K. C. McDonald, and F. T. Ulaby 1990
[8] Chris Oliver, Shaun Quegan, "Understanding Synthetic Aperture Radar Images", Artech. House, Boston, London, 1998
[9] Arsenault, H. H, and G. April, "Properties of Speckle Integrated with a Finite Aperture and Logarithmically Transformed," J. Opt. Soc. Amer., Vol. 66, 1976, pp. 1160-1163
[10] Lee,J.-S. , "A Simple Speckle Smoothing Algorithm for Synthetic Aperture Radar Images," IEEE Trans. System, Man and Cybernetics, Vol. 13, 1983, pp. 85-89
[11] Goodman,J.W., "Statistical Properties of Laser Speckle Patterns,"Laser Speckle and Related Phenomena, J. C. Dainty(ed-), New York:Springer-Verlag, 1984, pp.9-75
[12] Quegan,S., "interpolation and sampling in SAR images" IEEE Trans. On Geoscience and remote sensing vol28,1990,641-646
[13] W. Equitz and T. Cover, "Successive refinement of information,"IEEE Trans. Information Theory, Vol. 37,Mar. 1991,pp. 269-275
[14] A.Said and W.A.Pearlman, "An image multiresolution representation for lossless and lossy compression," IEEE Trans. Image Processing, vol.5, pp.1303-1310, Sept, 1996．
[15] M. Rabbani and P. W. Jones, "Digital Image Compression Techniques," Bellingham, WA: SPIE Opt. Eng. Press. 1991
[16] R. A. DeVore, B. Jawerth, and B. J. Lucier, "Image Compression Through Wavelet Transform Coding," IEEE Trans. Inform. Theory, Vol. 38, Mar. 1992, pp.719-746
[17] Shapiro J M. Embedded image coding using zerotree of wavelet coefficients. IEEE Trans. Signal Processing, 1993,41(12) :3445-3462．
[18] A.Said and W.A.Pearlman. Anew,fast,and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans .Circuits Syst.VideoTechnol,vol.6,pp.243-250,June 1996．
[19] Daubechies, I., Orthonormal bases of compactly supported wavelets, Communications on Pure and Applied mathematics, 1988, Vol. 41, No. 11, pp.909-996．
[20] Quegan,S., "interpolation and sampling in SAR images" IEEE Trans. On Geoscience and remote sensing vol28,1990,641-646
[21] Mallat, S., A theory for multiresolution signal decomposition:the wavelet representation, IEEE Trans. Pattern Analysis and machine Intelligence, 1989, Vol. 11, pp. 674-693．
[22] Cohen, A, Daubechies, I., and Feanvean, J., Bi-orthogonal bases of compactly supported wavelets. Comm.. Pure Appl. Math., 1992, Vol. 45, pp.485-560．
[23] Zhaohui Zeng,,Cumming Jan G, SAR image data compression using a tree-structured wavelet transform[J] IEEE Trans. Geoscience and Remote Sensing, 2001, 39(3) : 546-552
[24] Arsenault H. H. and April G, Properties of speckle integrated with a finite aperature and logarithmic transformation [M], Opt. Soc. Amer., 1976: 66-1160
[25] Unser, M., Approximation power of bi-orthogonal wavelet expansions, IEEE Trans, on signal Processing, 1996, Vol.44, pp.519-527．
[26] Rioul,O., Regular wavelets: a discrete-time approach, IEEE Trans, on Signal processing, 1993, Vol. 41, pp.3572-3579．
[27] Antonini, M., et. al., Image coding using wavelet transform, IEEE Trans. Image Proc., 1992, Vol. 1, pp. 205-220．
[28] Vetterli, M. and Herley, C, Wavelets and filter banks: Theory and design, IEEE Trans. Acoust. Speech signal proc., 1992, Vol.40, No.9, pp. 2207-2232．
[29] Villasenor, J., Belzer, B., Liao, J., Wavelet Filter Evaluation for Image Compression, IEEE Transactions on Image Processing, 1995, Vol. 2, pp. 1053-1060．
[30] M.J.Gormish,E.L.Schwart/,A.F.Keith,M.P.Boliek,and A.Zandi "Lossless and nearly lossless compression of high quality images," Proc. SPIE, vol. 3025, pp.62-70, Mar. 1997．
[31] A.R.Calderbank,I.Daubechies,W.Swedens,and B.L.Yeo,"Wavelet transforms that map integers to integers,"Appl.Comput.Harmon.Anal.,vol.5,pp.332-369,July 1998．
[32] M.D.Adams and F.Kossentini,"Low-complexity reversible integer-to-integer wavelet transforms for image coding,"in Proc.IEEE Pacific Rim Conf.Communication,Computers,Signal Processing, Victoria,B .C. Canada, Aug. 1999,pp 177-180．
[33] M.D.Adams,I.Kharitonenko,and F.Kossentini, Report on core experiment CodEff4: Performance evaluation of several reversible integer-to-integer wavelet transforms in the JPEG-2000 verification model(version 2． 1) ,ISO/IEC JTC 1/SC
29/WG 1 N1015．
[34]M.Antonini,M.Barlaud ,P. Mathieu,and I.Daubechies,"Image coding using wavelet tranform," IEEE Trans. Image Processing, vol. 1, no.2, pp.205-220, Apr. 1992.
[35]李世雄、刘家琦编著，小波变换和反演数据基础，北京：地质出版社，1994。
[36]郭华东，雷达对地观测理论与应用，北京：科学出版社，2000
[37]耿则勋，小波变换理论及在遥感影像压缩中的应用，北京：测绘出版社，2002
[38]张远鹏，董海，周文灵，计算机图象处理技术基础，北京：北京大学出版社，1996
[2] A. Grossman and J. morlet, Decomposition for Hardy Function into Square Integrabal Wavelets of Constant Shape SLAM, J. Math., 1984, vol. 15:723-736
[3] W. R. Zettler, et al, Application of Compactly Supported Wavelets to Image Compression , SPIE, Vol. 1244 Image Recognition Algorithm and Techniques 1990, 150-160
[4] M. Antonini, et al , Image Coding using Wavelet Transform ,IEEE, Trans. Image Proc., 1992, 1(2) :205-220
[5] Shapiro J M. Embedded image coding using zerotree of wavelet coefficients. IEEE Trans. Signal Processing, 1993,41 (12) :3445-3462．
[6] Lurie, J.B,B.W.Evans,B.Ringer,M.Yeats, image quality measures to assess hyperspectral compression techniques, Proceedings of Conference on Microwave Instrumentation and Satellite Photogrammetry for Remote Sensing of the Earth ,SPIE Vol.2313,1994,pp.2-14
[7] Ulaby, F. T., R. K. Moore, and A. K. Fung, 1986; Tsang, L., J. A. Kong, and R. T. Shin,1985; Fung A. K. 1994; Kong, J. A. 1990; Kuga, Y, M. W. Whitt, K. C. McDonald, and F. T. Ulaby 1990
[8] Chris Oliver, Shaun Quegan, "Understanding Synthetic Aperture Radar Images", Artech. House, Boston, London, 1998
[9] Arsenault, H. H, and G. April, "Properties of Speckle Integrated with a Finite Aperture and Logarithmically Transformed," J. Opt. Soc. Amer., Vol. 66, 1976, pp. 1160-1163
[10] Lee,J.-S. , "A Simple Speckle Smoothing Algorithm for Synthetic Aperture Radar Images," IEEE Trans. System, Man and Cybernetics, Vol. 13, 1983, pp. 85-89
[11] Goodman,J.W., "Statistical Properties of Laser Speckle Patterns,"Laser Speckle and Related Phenomena, J. C. Dainty(ed-), New York:Springer-Verlag, 1984, pp.9-75
[12] Quegan,S., "interpolation and sampling in SAR images" IEEE Trans. On Geoscience and remote sensing vol28,1990,641-646
[13] W. Equitz and T. Cover, "Successive refinement of information,"IEEE Trans. Information Theory, Vol. 37,Mar. 1991,pp. 269-275
[14] A.Said and W.A.Pearlman, "An image multiresolution representation for lossless and lossy compression," IEEE Trans. Image Processing, vol.5, pp.1303-1310, Sept, 1996．
[15] M. Rabbani and P. W. Jones, "Digital Image Compression Techniques," Bellingham, WA: SPIE Opt. Eng. Press. 1991
[16] R. A. DeVore, B. Jawerth, and B. J. Lucier, "Image Compression Through Wavelet Transform Coding," IEEE Trans. Inform. Theory, Vol. 38, Mar. 1992, pp.719-746
[17] Shapiro J M. Embedded image coding using zerotree of wavelet coefficients. IEEE Trans. Signal Processing, 1993,41(12) :3445-3462．
[18] A.Said and W.A.Pearlman. Anew,fast,and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans .Circuits Syst.VideoTechnol,vol.6,pp.243-250,June 1996．
[19] Daubechies, I., Orthonormal bases of compactly supported wavelets, Communications on Pure and Applied mathematics, 1988, Vol. 41, No. 11, pp.909-996．
[20] Quegan,S., "interpolation and sampling in SAR images" IEEE Trans. On Geoscience and remote sensing vol28,1990,641-646
[21] Mallat, S., A theory for multiresolution signal decomposition:the wavelet representation, IEEE Trans. Pattern Analysis and machine Intelligence, 1989, Vol. 11, pp. 674-693．
[22] Cohen, A, Daubechies, I., and Feanvean, J., Bi-orthogonal bases of compactly supported wavelets. Comm.. Pure Appl. Math., 1992, Vol. 45, pp.485-560．
[23] Zhaohui Zeng,,Cumming Jan G, SAR image data compression using a tree-structured wavelet transform[J] IEEE Trans. Geoscience and Remote Sensing, 2001, 39(3) : 546-552
[24] Arsenault H. H. and April G, Properties of speckle integrated with a finite aperature and logarithmic transformation [M], Opt. Soc. Amer., 1976: 66-1160
[25] Unser, M., Approximation power of bi-orthogonal wavelet expansions, IEEE Trans, on signal Processing, 1996, Vol.44, pp.519-527．
[26] Rioul,O., Regular wavelets: a discrete-time approach, IEEE Trans, on Signal processing, 1993, Vol. 41, pp.3572-3579．
[27] Antonini, M., et. al., Image coding using wavelet transform, IEEE Trans. Image Proc., 1992, Vol. 1, pp. 205-220．
[28] Vetterli, M. and Herley, C, Wavelets and filter banks: Theory and design, IEEE Trans. Acoust. Speech signal proc., 1992, Vol.40, No.9, pp. 2207-2232．
[29] Villasenor, J., Belzer, B., Liao, J., Wavelet Filter Evaluation for Image Compression, IEEE Transactions on Image Processing, 1995, Vol. 2, pp. 1053-1060．
[30] M.J.Gormish,E.L.Schwart/,A.F.Keith,M.P.Boliek,and A.Zandi "Lossless and nearly lossless compression of high quality images," Proc. SPIE, vol. 3025, pp.62-70, Mar. 1997．
[31] A.R.Calderbank,I.Daubechies,W.Swedens,and B.L.Yeo,"Wavelet transforms that map integers to integers,"Appl.Comput.Harmon.Anal.,vol.5,pp.332-369,July 1998．
[32] M.D.Adams and F.Kossentini,"Low-complexity reversible integer-to-integer wavelet transforms for image coding,"in Proc.IEEE Pacific Rim Conf.Communication,Computers,Signal Processing, Victoria,B .C. Canada, Aug. 1999,pp 177-180．
[33] M.D.Adams,I.Kharitonenko,and F.Kossentini, Report on core experiment CodEff4: Performance evaluation of several reversible integer-to-integer wavelet transforms in the JPEG-2000 verification model(version 2． 1) ,ISO/IEC JTC 1/SC
29/WG 1 N1015．
[34]M.Antonini,M.Barlaud ,P. Mathieu,and I.Daubechies,"Image coding using wavelet tranform," IEEE Trans. Image Processing, vol. 1, no.2, pp.205-220, Apr. 1992.
[35]李世雄、刘家琦编著，小波变换和反演数据基础，北京：地质出版社，1994。
[36]郭华东，雷达对地观测理论与应用，北京：科学出版社，2000
[37]耿则勋，小波变换理论及在遥感影像压缩中的应用，北京：测绘出版社，2002
[38]张远鹏，董海，周文灵，计算机图象处理技术基础，北京：北京大学出版社，1996