基于脊波双框架系统的图像融合和机场目标检测
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摘要
寻求图像尤其是自然图像的“稀疏”表示方法,一直以来都是数学、计算机视觉及数据压缩等领域专家学者研究的一个热点。小波变换的不足使得人们不断寻求更好的非线性逼近工具,脊波理论就在这样的背景下应运而生。脊波双框架系统一方面继承了正交脊波将线奇异转化为点奇异的核心思想,能有效的处理图像中的线奇异,另一方面又充分利用了现有的各种小波族。本文在深入研究脊波双框架系统的基础上,将其应用于图像融合、直线检测和机场检测等问题。主要工作概括如下:
将脊波双框架系统和Curvelet双框架系统用于图像融合。根据脊波双框架变换子带间的方向性,提出了一种基于方向信息的局部方差的融合规则,并用于多聚焦、医学、遥感图像的融合问题,实验结果表明,其融合效果令人较为满意,尤其在融合后边缘等细节区域效果有所提高;根据传统方法检测直线的不足之处,将基波双框架用于直线检测,提出了一种结合脊波双框架系统的局部直线检测方法,实验结果表明,本文方法能够较精确的检测出直线的方向和位置,并且能够有效地抑制噪声的干扰;将脊波双框架系统应用于SAR图像机场目标检测之中,先对待检测图像进行简单的预处理,然后用脊波双框架系统对预处理以后的图像进行直线特征检测,检测到具有直线特征的跑道,然后再进行直线跟踪和二值化处理得到检测结果。实验结果表明,该算法实现简单,不需要复杂的后处理过程,而且可以较为准确的检测到机场主跑道。
It is of great importance to find methods that can sparsely represent natural images for researchers in the fields of mathematics, computer vision and data compression. Motivated by the failure of wavelet, much work has been done to look for new systems superior to separable wavelet systems. Ridgelet theory was developed under such a background. A new image representation system referred to as ridgelet bi-frame is developed, which not only inherits the key idea of the orthonormal ridgelet, but also provides a more generalized notion. Apply the ridgelet bi-frame to linear feature detection, Image fusion and airport detection is the main work in this paper. The research results included in this article are as follows:
The papers apply the ridgelet bi-frame and curvelet bi-frame to images fusion. Based on the directional properties of ridgelet bi-frame subband, a new method for anisotropic images fusion method is presented, which combines with local variance of subband. The method is respectively applied to the multifocus, the medical and the remote image fusions in the experiments. Experiments show that they have achieved satisfactory results, especially in edge. Considering the problems for linear feature detection, a novel one based on ridgelet bi-frame for localized linear feature detection is given. All kinds of experiments show that the linear feature detection method based on ridgelet bi-frame is able to accurately detect the direction and position of a straight line, and can effectively suppress noise. we propose a new airport detection method for SAR images based on ridgelet bi-frame. At First, treat a simple preprocessing to images, and then extract straight lines form edge images, finally line tracking and binarization are employed. The experimental results show that the new algorithm is speedy and simple, meanwhile, it does not require complicated post-processing.
将脊波双框架系统和Curvelet双框架系统用于图像融合。根据脊波双框架变换子带间的方向性,提出了一种基于方向信息的局部方差的融合规则,并用于多聚焦、医学、遥感图像的融合问题,实验结果表明,其融合效果令人较为满意,尤其在融合后边缘等细节区域效果有所提高;根据传统方法检测直线的不足之处,将基波双框架用于直线检测,提出了一种结合脊波双框架系统的局部直线检测方法,实验结果表明,本文方法能够较精确的检测出直线的方向和位置,并且能够有效地抑制噪声的干扰;将脊波双框架系统应用于SAR图像机场目标检测之中,先对待检测图像进行简单的预处理,然后用脊波双框架系统对预处理以后的图像进行直线特征检测,检测到具有直线特征的跑道,然后再进行直线跟踪和二值化处理得到检测结果。实验结果表明,该算法实现简单,不需要复杂的后处理过程,而且可以较为准确的检测到机场主跑道。
It is of great importance to find methods that can sparsely represent natural images for researchers in the fields of mathematics, computer vision and data compression. Motivated by the failure of wavelet, much work has been done to look for new systems superior to separable wavelet systems. Ridgelet theory was developed under such a background. A new image representation system referred to as ridgelet bi-frame is developed, which not only inherits the key idea of the orthonormal ridgelet, but also provides a more generalized notion. Apply the ridgelet bi-frame to linear feature detection, Image fusion and airport detection is the main work in this paper. The research results included in this article are as follows:
The papers apply the ridgelet bi-frame and curvelet bi-frame to images fusion. Based on the directional properties of ridgelet bi-frame subband, a new method for anisotropic images fusion method is presented, which combines with local variance of subband. The method is respectively applied to the multifocus, the medical and the remote image fusions in the experiments. Experiments show that they have achieved satisfactory results, especially in edge. Considering the problems for linear feature detection, a novel one based on ridgelet bi-frame for localized linear feature detection is given. All kinds of experiments show that the linear feature detection method based on ridgelet bi-frame is able to accurately detect the direction and position of a straight line, and can effectively suppress noise. we propose a new airport detection method for SAR images based on ridgelet bi-frame. At First, treat a simple preprocessing to images, and then extract straight lines form edge images, finally line tracking and binarization are employed. The experimental results show that the new algorithm is speedy and simple, meanwhile, it does not require complicated post-processing.
引文
[1]焦李成,王爽,等.自然计算、机器学习与图像理解前沿.西安电子科技大学出版社,2008.
[2] X. Xue, X. Wu. Image representation based on multi-scale edge compensation. IEEE Internat. Conf. on Image Processing, 1999.
[3] M. N. Do. Directional Multiresolution Image Representations. PhD thesis, Swiss Federal Institute of Technology, Lausanne, Switzerland, December 2001.
[4]谭冠军.基于图像分层表示和超完备Contourlet的图像去噪.西安电子科技大学硕士学士论文,2008.
[5]焦李成,谭山.图像的多尺度儿何分析:回顾和展望[J].电子学报,2003,31(12A):1975-1981.
[6]侯彪,刘芳,焦李成.基于脊波变换的直线特征检测[J].中国科学,2003,33(1):65-73.
[7] E. J. Candès. Ridgelet: Theory and Applications. Ph. D. Technical Report, Department of Statistics, Stanford University, 1998.
[8] E J, Candes, Monoscale Ridgelet for the representation of images with edges, Dept. Statist., Stanford Univ., Stanford, CA, Tech. Rep., 1999.
[9] E. J. Candes and D. L .Donoho, Curvelet——A surprisingly effective nonadaptive representation for objects with edges, In: Curve and Surface Fitting: Saint-Malo 1999, A. Cohen, C. Rabut, and L. L. Schumaker, eds. (Nashville, TN: Van- derbilt Univ. Press, 1999).
[10] Erwan Le Pennec and Stéphane Mallat. Sparse Geometric Image Representations With Bandelets. IEEE Trans on Image Processing. vol. 14, no. 4, pp. 423-438, 2005.
[11] Francois G. Meyer and Ronald R. Coifman. Brushlets: A Tool for Directional Image Analysis and Image Compression. Applied and Computational Harmonic Analysis. vol. 4, pp. 147-187, 1997.
[12] Minh N. Do and Martin Vetterli. The Contourlet Transform: An Efficient directional Multiresolution Image Representation. IEEE Trans on Image Processing. vol. 14, no. 12, pp. 2091-2106, 2005.
[13] Stephane Mallat.信号处理的小波导引.机械工业出版社,2002.
[14]崔锦泰.小波分析导引.西安交通大学出版社,1995.
[15]刘贵忠,邸双亮.小波分析及其应用第一版.西安电子科技大学出版社,1992. pp. 1-35.
[16]程正兴等.小波分析算法与应用第一版.西安交通大学出版社,1998.pp.57-70.
[17] E. J. Candès. Ridgelet, Harmonic analysis of neural networks, Appl. Comput. Harmon. Anal, 6: 197-218, 1999.
[18] D. L. Donoho. Orthonormal ridgelets and linear singularities. Report no.1998-19, Department of Statistics, Stanford University, 1998.
[19] David L. Donoho, Mark R. Duncan, Digital Curvelet Transform: Strategy, Implementation and Experiments, Stanford Univ., Stanford, CA, Tech. Rep., 1999.
[20] E. J Candes, D. L. Donoho,“Curvelets”, Tech. Report, Department of Statistics, Stanford University, 1999.
[21] D. L. Donoho, Orthonormal ridgelets and linear singularities, Tech. Report, Department of Statistics, Atanford University, 1998.
[22] Do M N. Directional multiresolution image representations[D]. Federal Institute of Technology, Switzerland, 2001. 12.
[23] E. J. Candes, D. L. Donoho. Curvelets[R]. USA: Department of Statistics. Stanford University, 1999.
[24] J. L. Starck, E. J. Candes and D. L. Donoho, The curvelet transform for image denoising, IEEE Trans. Image Processing,11: 670-684, 2002.
[25]谭山.脊波双框架系统与自然图像的多变量统计模型.西安电子科技大学,2006.12.
[26] S. Tan and L. Jiao, Ridgelet Bi-frame, Applied and Computational Harmonic Analysis, 20, pp. 391- 402, 2006.
[27] S. Tan and L. C. Jiao, Image Denoising Using the Ridgelet Bi-frame, J. Opt. Soc. Amer. A, vol. 23, pp. 2449-2461, 2006.
[28] S. Tan, X. R. Zhang and L. C. Jiao, Dual Ridgelet Frame Constucted Using Biorthonormal Wavelet Basis, In: Proceeding of IEEE International Conference on Acoustics, Speech, and Singal Processing, March 19-23, Philadelphia, PA, USA, 2005, pp.997-1000.
[29] S. Tan, X. R. Zhang and L. C. Jiao, Monoscale Dual Ridgelet Frame, In: Proceedings of International Conference on Image Analysis and Recognition, ICIAR 2005, Toronto, Canada, September 28-30, 2005, Lecture Notes in Computer Science, Vol. 3449, pp. 263-269.
[30] S. Tan and L. C. Jiao, Statistical Models for Natural Images in the Ridgelet Bi-frame Domain, submitted to pattern Recognition, 2006.
[31] Copeland A. C., Ravichandran G., Trivedi M. M. Localized Radon transform based detection of ship wakes in SAR images. IEEE Trans. On Geoscience and Remote Sensing. Vol. 33, No.1, Jan. 1995: 35-45.
[32] Averbuch A, Coifman R, Donoho D L, et al. Fast Slant Stack: A notion of Radon Transform for Data in a Cartesian Grid which is Rapidly Computible, Algebraically Excat, Geometrically Faithful and Invertible. http://www-stat-stanford/ ~donoho /Reports.
[33] B. A. Olshausen and D. J. Field, Emergence of simple-cell receptive field properties by learning a sparse code for natural images, Nature, 381: 607-609, 1996.
[34] B. A. Olshausen and D. J. Field, Sparse coding with an overcomplete basis set: A strategy employed by V1? Vision Res., 37: 3311-3325, 1997.
[35] S. Tan and L. Jiao, New evidences for sparse coding strategy employed in visual neurons: form the image processing and nonlinear approximation viewpoint, in: Proceedings of the 13th European Symposium on Artificial Neural Networks, April 27-29, 2005, Bruges, Belgium.
[36]侯彪.脊波和方向信息检测方法及应用.西安电子科技大学,2003. 4.
[37]焦李成,张向荣,等.智能SAR图像理解与解译.北京:科学出版社,2008.
[38] Chavez P S, et al. Comparison of three different methods to merging to merge multiresolution and multispectral data, landsat TM and SPOT panchromatic. PE&RS, 1991, 57(3): 265~303.
[39] Pellemans A H J M, Jorddans R W L, Allewiijin R. Merging unltispectral and panchromatic SPOT images with respect to the radiometric properties of the sensor. PE&RS, 1993, 59(1): 81~87.
[40] Hayden R, Dalke G W, Henkel J, et al. Application of the HIS color transform to the processing of multisensor data and image enhancement. Proc. of the International Symposium on Remote Sensing of Arid and Semi-arid Lands, Cairo, Egypt, 1982: 599~616.
[41] Yesou H, Besnus Y, Rolet Y. Extraction of spectral information from Landsat TM data and merger with SPOT panchromatic imagery—a contribution to the study of geological structures. ISPRS Journal of Photogrammetry and Remote Sensing, 1993, 48(5): 23~36.
[42] Ehlers M. Multisensor image fusion techniques in remote sensing. ISPRS Journal of Photogrammetry and Remote sensing, 1991, 46: 19~30.
[43] Nunez K, Otazu X. Multiresolution–based image fusion with additive waveletrepresentation. IEEE Trans. Geosience and remoteSensing, 1999, 37(3): 1204~1211.
[44] Li H, Manjunath B S, Mitra S K. Multisensor image fusion using the wavelet transform. Graphical Models and Image Processing, 1995, 27(3): 235~244.
[45] M. N. Do, Directional multiresolution image represntations. EPFL, 2001.
[46] M. N. Do, M. Vetterli. Contourlets: A directional multiresolution image representation. International Conference on Image Processing, 2002, 1: I-357~360.
[47] Po D D Y, Do M N. Directional multiscale modeling of images using the contourlet transform. IEEE Workshop on Statistical Signal Processing, 2003: 262~265.
[48] Do M N, Vetterli M. Contourlets: A new directional multiresolution image representation. Conference Record of the Thirty-sixth Asilomar Conference on Signals, Systems and Computers, 2002, 1: 497~501.
[49] S. Mallat, A Wavelet Tour of Signal Processing. 2nd ed. (Academic Press, 1999).
[50] A. Cohen, I. Daubechies, and J. C. Feauveau, Biothogonal bases of compactly supported wavelets. Commun. On Pure and Appl. Math., 45: 484-560, 1992.
[51] Yang M., Lee J.-S., Lien C.-C., Huang C.-L. Hough transform modified by line connectivity and line thickness. IEEE Trans. on Pattern Analysis and Machine intelligence, Vol. 19, No. 8, Aug. 1997: 905-910.
[52]舒宁.雷达遥感原理.北京:测绘出版社,1997.
[53]邵芸.合成孔径雷达.科学出版社,2001.
[54]保铮,刑孟道,王彤.雷达成像技术.电子工业出版社,2005.
[55] Michel A. Airport detection using a simple model, multi-source images and altimetric information[J]. SPIE, 1998, (2315): 604~615.
[56] Way J, Atwood S E. The evolution of synthetic aperture radar systems and their progression to the EOS SAR.IEEE Trans. Geoscience and Remote Sensing, 1991, 29(6): 962~985.
[57]李强,王正志.基于小波分析的噪声抑制和数据压缩综合技术——SAR图像的噪声抑制和数据压缩.系统工程与电子技术, 1998, 12: 15~17.
[58] Odegard J.Guo H, Burrus C. Wavelet based SAR speckle reduction and image compression. Proc. of SPIE, 1995, 4:17~21.
[59] S. Mallat, S. Zhong. Characterization of Signals from Multiscale Edges. IEEE Trans. On Pattern Analysis and Machine Intelligence. Vol. 12, pp629~639, July 1990.
[60] Mallat S. A theory formultiresolution signal decomposition[J]. The Wavelet Representation, IEEE Trans, On PAML, 1989, 11 (7) : 674~693.
[61]章毓.图像处理和分析.北京:清华大学出版社,1999.
[2] X. Xue, X. Wu. Image representation based on multi-scale edge compensation. IEEE Internat. Conf. on Image Processing, 1999.
[3] M. N. Do. Directional Multiresolution Image Representations. PhD thesis, Swiss Federal Institute of Technology, Lausanne, Switzerland, December 2001.
[4]谭冠军.基于图像分层表示和超完备Contourlet的图像去噪.西安电子科技大学硕士学士论文,2008.
[5]焦李成,谭山.图像的多尺度儿何分析:回顾和展望[J].电子学报,2003,31(12A):1975-1981.
[6]侯彪,刘芳,焦李成.基于脊波变换的直线特征检测[J].中国科学,2003,33(1):65-73.
[7] E. J. Candès. Ridgelet: Theory and Applications. Ph. D. Technical Report, Department of Statistics, Stanford University, 1998.
[8] E J, Candes, Monoscale Ridgelet for the representation of images with edges, Dept. Statist., Stanford Univ., Stanford, CA, Tech. Rep., 1999.
[9] E. J. Candes and D. L .Donoho, Curvelet——A surprisingly effective nonadaptive representation for objects with edges, In: Curve and Surface Fitting: Saint-Malo 1999, A. Cohen, C. Rabut, and L. L. Schumaker, eds. (Nashville, TN: Van- derbilt Univ. Press, 1999).
[10] Erwan Le Pennec and Stéphane Mallat. Sparse Geometric Image Representations With Bandelets. IEEE Trans on Image Processing. vol. 14, no. 4, pp. 423-438, 2005.
[11] Francois G. Meyer and Ronald R. Coifman. Brushlets: A Tool for Directional Image Analysis and Image Compression. Applied and Computational Harmonic Analysis. vol. 4, pp. 147-187, 1997.
[12] Minh N. Do and Martin Vetterli. The Contourlet Transform: An Efficient directional Multiresolution Image Representation. IEEE Trans on Image Processing. vol. 14, no. 12, pp. 2091-2106, 2005.
[13] Stephane Mallat.信号处理的小波导引.机械工业出版社,2002.
[14]崔锦泰.小波分析导引.西安交通大学出版社,1995.
[15]刘贵忠,邸双亮.小波分析及其应用第一版.西安电子科技大学出版社,1992. pp. 1-35.
[16]程正兴等.小波分析算法与应用第一版.西安交通大学出版社,1998.pp.57-70.
[17] E. J. Candès. Ridgelet, Harmonic analysis of neural networks, Appl. Comput. Harmon. Anal, 6: 197-218, 1999.
[18] D. L. Donoho. Orthonormal ridgelets and linear singularities. Report no.1998-19, Department of Statistics, Stanford University, 1998.
[19] David L. Donoho, Mark R. Duncan, Digital Curvelet Transform: Strategy, Implementation and Experiments, Stanford Univ., Stanford, CA, Tech. Rep., 1999.
[20] E. J Candes, D. L. Donoho,“Curvelets”, Tech. Report, Department of Statistics, Stanford University, 1999.
[21] D. L. Donoho, Orthonormal ridgelets and linear singularities, Tech. Report, Department of Statistics, Atanford University, 1998.
[22] Do M N. Directional multiresolution image representations[D]. Federal Institute of Technology, Switzerland, 2001. 12.
[23] E. J. Candes, D. L. Donoho. Curvelets[R]. USA: Department of Statistics. Stanford University, 1999.
[24] J. L. Starck, E. J. Candes and D. L. Donoho, The curvelet transform for image denoising, IEEE Trans. Image Processing,11: 670-684, 2002.
[25]谭山.脊波双框架系统与自然图像的多变量统计模型.西安电子科技大学,2006.12.
[26] S. Tan and L. Jiao, Ridgelet Bi-frame, Applied and Computational Harmonic Analysis, 20, pp. 391- 402, 2006.
[27] S. Tan and L. C. Jiao, Image Denoising Using the Ridgelet Bi-frame, J. Opt. Soc. Amer. A, vol. 23, pp. 2449-2461, 2006.
[28] S. Tan, X. R. Zhang and L. C. Jiao, Dual Ridgelet Frame Constucted Using Biorthonormal Wavelet Basis, In: Proceeding of IEEE International Conference on Acoustics, Speech, and Singal Processing, March 19-23, Philadelphia, PA, USA, 2005, pp.997-1000.
[29] S. Tan, X. R. Zhang and L. C. Jiao, Monoscale Dual Ridgelet Frame, In: Proceedings of International Conference on Image Analysis and Recognition, ICIAR 2005, Toronto, Canada, September 28-30, 2005, Lecture Notes in Computer Science, Vol. 3449, pp. 263-269.
[30] S. Tan and L. C. Jiao, Statistical Models for Natural Images in the Ridgelet Bi-frame Domain, submitted to pattern Recognition, 2006.
[31] Copeland A. C., Ravichandran G., Trivedi M. M. Localized Radon transform based detection of ship wakes in SAR images. IEEE Trans. On Geoscience and Remote Sensing. Vol. 33, No.1, Jan. 1995: 35-45.
[32] Averbuch A, Coifman R, Donoho D L, et al. Fast Slant Stack: A notion of Radon Transform for Data in a Cartesian Grid which is Rapidly Computible, Algebraically Excat, Geometrically Faithful and Invertible. http://www-stat-stanford/ ~donoho /Reports.
[33] B. A. Olshausen and D. J. Field, Emergence of simple-cell receptive field properties by learning a sparse code for natural images, Nature, 381: 607-609, 1996.
[34] B. A. Olshausen and D. J. Field, Sparse coding with an overcomplete basis set: A strategy employed by V1? Vision Res., 37: 3311-3325, 1997.
[35] S. Tan and L. Jiao, New evidences for sparse coding strategy employed in visual neurons: form the image processing and nonlinear approximation viewpoint, in: Proceedings of the 13th European Symposium on Artificial Neural Networks, April 27-29, 2005, Bruges, Belgium.
[36]侯彪.脊波和方向信息检测方法及应用.西安电子科技大学,2003. 4.
[37]焦李成,张向荣,等.智能SAR图像理解与解译.北京:科学出版社,2008.
[38] Chavez P S, et al. Comparison of three different methods to merging to merge multiresolution and multispectral data, landsat TM and SPOT panchromatic. PE&RS, 1991, 57(3): 265~303.
[39] Pellemans A H J M, Jorddans R W L, Allewiijin R. Merging unltispectral and panchromatic SPOT images with respect to the radiometric properties of the sensor. PE&RS, 1993, 59(1): 81~87.
[40] Hayden R, Dalke G W, Henkel J, et al. Application of the HIS color transform to the processing of multisensor data and image enhancement. Proc. of the International Symposium on Remote Sensing of Arid and Semi-arid Lands, Cairo, Egypt, 1982: 599~616.
[41] Yesou H, Besnus Y, Rolet Y. Extraction of spectral information from Landsat TM data and merger with SPOT panchromatic imagery—a contribution to the study of geological structures. ISPRS Journal of Photogrammetry and Remote Sensing, 1993, 48(5): 23~36.
[42] Ehlers M. Multisensor image fusion techniques in remote sensing. ISPRS Journal of Photogrammetry and Remote sensing, 1991, 46: 19~30.
[43] Nunez K, Otazu X. Multiresolution–based image fusion with additive waveletrepresentation. IEEE Trans. Geosience and remoteSensing, 1999, 37(3): 1204~1211.
[44] Li H, Manjunath B S, Mitra S K. Multisensor image fusion using the wavelet transform. Graphical Models and Image Processing, 1995, 27(3): 235~244.
[45] M. N. Do, Directional multiresolution image represntations. EPFL, 2001.
[46] M. N. Do, M. Vetterli. Contourlets: A directional multiresolution image representation. International Conference on Image Processing, 2002, 1: I-357~360.
[47] Po D D Y, Do M N. Directional multiscale modeling of images using the contourlet transform. IEEE Workshop on Statistical Signal Processing, 2003: 262~265.
[48] Do M N, Vetterli M. Contourlets: A new directional multiresolution image representation. Conference Record of the Thirty-sixth Asilomar Conference on Signals, Systems and Computers, 2002, 1: 497~501.
[49] S. Mallat, A Wavelet Tour of Signal Processing. 2nd ed. (Academic Press, 1999).
[50] A. Cohen, I. Daubechies, and J. C. Feauveau, Biothogonal bases of compactly supported wavelets. Commun. On Pure and Appl. Math., 45: 484-560, 1992.
[51] Yang M., Lee J.-S., Lien C.-C., Huang C.-L. Hough transform modified by line connectivity and line thickness. IEEE Trans. on Pattern Analysis and Machine intelligence, Vol. 19, No. 8, Aug. 1997: 905-910.
[52]舒宁.雷达遥感原理.北京:测绘出版社,1997.
[53]邵芸.合成孔径雷达.科学出版社,2001.
[54]保铮,刑孟道,王彤.雷达成像技术.电子工业出版社,2005.
[55] Michel A. Airport detection using a simple model, multi-source images and altimetric information[J]. SPIE, 1998, (2315): 604~615.
[56] Way J, Atwood S E. The evolution of synthetic aperture radar systems and their progression to the EOS SAR.IEEE Trans. Geoscience and Remote Sensing, 1991, 29(6): 962~985.
[57]李强,王正志.基于小波分析的噪声抑制和数据压缩综合技术——SAR图像的噪声抑制和数据压缩.系统工程与电子技术, 1998, 12: 15~17.
[58] Odegard J.Guo H, Burrus C. Wavelet based SAR speckle reduction and image compression. Proc. of SPIE, 1995, 4:17~21.
[59] S. Mallat, S. Zhong. Characterization of Signals from Multiscale Edges. IEEE Trans. On Pattern Analysis and Machine Intelligence. Vol. 12, pp629~639, July 1990.
[60] Mallat S. A theory formultiresolution signal decomposition[J]. The Wavelet Representation, IEEE Trans, On PAML, 1989, 11 (7) : 674~693.
[61]章毓.图像处理和分析.北京:清华大学出版社,1999.