小波和支持向量机及其在图像压缩中的应用研究
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摘要
图像压缩是图像存储、传输的基础。原始图像数据存储空间较大,不利于存储、传输。为了减小图像数据的存储空间和通信带宽,实现数据实时处理、显示和传输,需要对原始图像进行高效压缩。图像压缩编码可分为无损压缩编码和有损压缩编码。经典压缩算法理论已比较成熟。近来,又出现新的基于小波变换的压缩方法、分形压缩方法和神经网络压缩方法,称为第二代图像压缩编码方法,其具有更高的压缩比和图像恢复质量,受到越来越多的重视,但由于理论还不完善,在实际应用中仍存在许多问题。针对图像压缩的现状,本文结合支持向量回归与小波理论对图像压缩进行了研究,主要工作如下:
(1)研究了支持向量回归与DCT变换相结合的图像压缩方法,并通过实验论证了其可行性。
(2)我们结合SPIHT结构,提出一种支持向量回归与小波变换相结合的灰度图像压缩方法。该方法先将原始图像进行离散小波变换,得到多分辨率小波图像,再通过SPIHT结构进行小波系数重组,然后对每棵树上的小波系数进行支持向量回归,获得一系列支持向量和相应的权值,通过较少的支持向量拟合原始小波系数而达到数据压缩目的。
(3)研究了3DSPIHT的支持向量回归小波多光谱遥感图像压缩方法。在二维SPIHT支持向量回归小波图像压缩的基础之上,将压缩方法扩展到3DSPIHT,先对多波段光谱数据进行空间小波变换,再用3DSPIHT结构进行系数重组,然后通过支持向量回归进行图像压缩。实验结果表明,此方法可取得较好的效果,但压缩中,支持向量回归时间,压缩时间较长是一个有待解决的问题。
Efficient encoding algorithm is the key for image storage and transmission. Original image data needs huge storage space, and is unfavorable to store and transmit.To decrease the image storage space and realize real-time data process, it needs a high-perfomance image compression algorithm. Image compression code is divided into loseless compression and lossy compression.The classical image compression algorithm has already been sucessfully developed. Lately, some new compression method is deeply researched, such as image code based on wavelet transform, fractal theory and neural networks, which is called as the second-generation image code method, and are becoming increasingly concerned as a result of its higher-quality image compression effect. But because of their faulty theory, there are still many defects in factual application. According to research states of image compression,we deeply research image compression algorithm based on support vector regression and wavelet transform, and the main works are described as following.
(1) We deeply research an image compression algorithm of combining support vector regression and discrete cosine transform, and experimental results show its validity.
(2) Combining SPIHT structure, we propose a gray image compression algorithm based on SVR and wavelet transform. First, Original image data is decomposed by wavelet transform to gain multiresolution image data. Secondly, wavelet coefficients are resorted by using the SPIHT structure, and then we use support vector regression to process these wavelet coefficients on each SPIHT to obtain a series of support vectors and their corresponding weight value. At last Less support vectors are used to fit the primitive wavelet coefficients, thus the target of data compression is achieved.
(3) Combining 3DSPIHT structure, we research a multi-spectral remote-sensing image compression algorithm of combing SVR and wavelet transform. Based on image compression algorithm with two-dimensional SPIHT coefficient trees, we extend it to image compression algorithm with 3DSPIHT. The multi-spectral remote-sensing image are decomposed by two-dimensional wavelet transform, and then their wavelet coefficients are reorganized and resorted by 3DSPIHT structure, and lastly are compressed by support vector regression. Experimental results show this method may gain preferable effects. But in Data Compression, longer processing time of support vector regression and image compression need be solved in future research.
(1)研究了支持向量回归与DCT变换相结合的图像压缩方法,并通过实验论证了其可行性。
(2)我们结合SPIHT结构,提出一种支持向量回归与小波变换相结合的灰度图像压缩方法。该方法先将原始图像进行离散小波变换,得到多分辨率小波图像,再通过SPIHT结构进行小波系数重组,然后对每棵树上的小波系数进行支持向量回归,获得一系列支持向量和相应的权值,通过较少的支持向量拟合原始小波系数而达到数据压缩目的。
(3)研究了3DSPIHT的支持向量回归小波多光谱遥感图像压缩方法。在二维SPIHT支持向量回归小波图像压缩的基础之上,将压缩方法扩展到3DSPIHT,先对多波段光谱数据进行空间小波变换,再用3DSPIHT结构进行系数重组,然后通过支持向量回归进行图像压缩。实验结果表明,此方法可取得较好的效果,但压缩中,支持向量回归时间,压缩时间较长是一个有待解决的问题。
Efficient encoding algorithm is the key for image storage and transmission. Original image data needs huge storage space, and is unfavorable to store and transmit.To decrease the image storage space and realize real-time data process, it needs a high-perfomance image compression algorithm. Image compression code is divided into loseless compression and lossy compression.The classical image compression algorithm has already been sucessfully developed. Lately, some new compression method is deeply researched, such as image code based on wavelet transform, fractal theory and neural networks, which is called as the second-generation image code method, and are becoming increasingly concerned as a result of its higher-quality image compression effect. But because of their faulty theory, there are still many defects in factual application. According to research states of image compression,we deeply research image compression algorithm based on support vector regression and wavelet transform, and the main works are described as following.
(1) We deeply research an image compression algorithm of combining support vector regression and discrete cosine transform, and experimental results show its validity.
(2) Combining SPIHT structure, we propose a gray image compression algorithm based on SVR and wavelet transform. First, Original image data is decomposed by wavelet transform to gain multiresolution image data. Secondly, wavelet coefficients are resorted by using the SPIHT structure, and then we use support vector regression to process these wavelet coefficients on each SPIHT to obtain a series of support vectors and their corresponding weight value. At last Less support vectors are used to fit the primitive wavelet coefficients, thus the target of data compression is achieved.
(3) Combining 3DSPIHT structure, we research a multi-spectral remote-sensing image compression algorithm of combing SVR and wavelet transform. Based on image compression algorithm with two-dimensional SPIHT coefficient trees, we extend it to image compression algorithm with 3DSPIHT. The multi-spectral remote-sensing image are decomposed by two-dimensional wavelet transform, and then their wavelet coefficients are reorganized and resorted by 3DSPIHT structure, and lastly are compressed by support vector regression. Experimental results show this method may gain preferable effects. But in Data Compression, longer processing time of support vector regression and image compression need be solved in future research.
引文
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2.崔锦泰(程正兴泽).小波分析导论[M].西安:西安交通大学出版社,1995.
3. Falconer K著-曾文曲译.分形几何数学基础及应用[M].东北工学院出版社,1991.14—40
4. Vladimir N Vapnik著.张学工译.统计学习理论的本质[M].清华大学出版社,2000.
5. [美]Dooglss M.Bates,[加]Donald G.Watts.非线性回归分析及其应用[M].北京:中国统计出版社,1997.
6. Hou H S.A fast recursive algromthm for computing the discrete costne transtion[J].IEEE Trans.ASSP.1987,85:1455-1861.
7. Burges C.J.C.A Tutorial on Support Vector Machines for Pattern Recognition[J]. Knowledge Discovery and Data Mining, 1998,2(2):121-167.
8. Steve Gunn.Support Vector Machines for Classification and Regression[R]. ISIS Technical Re-port. University of Southampton,1998.
9. A J.Smola,B.Scholkopf. A Tutouial on Support Vector Regression[R].Neuro COLT2 TcchnicalReport Series. 1998.NC2-TR-1998-030.
10. V.Vapnik,S.Golowich,A.Smola.Support Vector Method for Function Approximation,Regression Estimation,and Signal Processing[R].In Advances in Neural Information Processing Systems 9,1996.
11. Cortes C, Vapnik V. Support Vector Networks[J]. Machine Learning, 1995. 20: 273-297.
12. Osuna E. E., Freund R., Girosi F. Support Vector Machines: Training and Applications A.I.[Z].MIT Artificial Intelligence Laboratory, 1997.
13. Osuna E, Freund R, Girosi F. An Inproved Training Algorithm for Support Vector Machines[J]. Workshop on Neural Networks for Signal Processing, New York: IEEE, 1997, 276-285.
14. Joachims T. Making Large-Scale SVM Learning Practical[M]. Advances in Kernel Methods—Support Vector Learning, Cambridge, MA: MIT Press, 1998, 169-184.
15. Platt J C. Fast Training of SVM Using Sequential Minimal Optimization[M]. Advances in Kernel Methods—Support Vector Learning, Cambridge, MA: MIT Press, 1998, 185-208.
16. Cristianini N,etc.Dynamically Adapting Kernels in Support Vector Machines[R]. Neuro COLT:[Technical Report TR-1998-017]. Royal Holloway College, 1998.
17. Tsuda K. Optimal Hyperplane Classifier with Adaptive Norm [ETL] .Technical report TR-99-9,1999.
18. Pontil M, etc. On the Noise Model of Support Vector Machine Regression[J]. CBCL Paper
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19. I.Guyon,N.Matic,and V.N.Vapnik et al.Discovering Informative Patterns and Data Cleaning[M]. In Advances in Knowledge Discovery and DataMining,U.M. Fayyad et al.,Eds.Cambridge,MA:MIT Press,1996.
20. R.Herbrich and J.Weston. Adaptive Margin Support Vector Machines fof Classification[J]. Inproc 9th ICANN, 1999,2:880-885.
21. G.Kollios,D.Gunopulos,N,Koudas,etc.Efficient Biased Sampling for Approximate Clussteringand Outlier Detection in Large Data Sets[J]. IEEE Trans. On Knowledge and Data Engineering. 2003, 15(5):1170-1187.
22. Zhang Xuegong.Using Class-center Vectors to Build Support Vector Machines[A]. Proceedingsof the 1999 IEEE Signal Processomg Society Workshop Neural Networks for Signal IX [C].Madison,WI, USA:1999,3-11.
23. Hung Han-Pang, Liu Yi-Hung. Fuzzy Support Vector Machines for Pattern Recognition and Data Mining[J].International Journal of Fuzzy Systems, 2002 ;4(3) : 826-835.
24. Lin chunfu,Wang Shengde.Fuzzy Support Vector Machines[J]. IEEE Transactions on Neural Networks, 2002,13(2):464-471.
25. Ruping S. Incremental Learning with Support Vector Machine[A].ICDM[C].2001:641-642.
26. Fung G, Mangasarian OL. Incremental Support Vector Machine Classification[R].Madison, Wisconsin,2001.
27.李凯,黄厚宽.支持向量机增量学习算法研究[J],北方交通大学学报,VO(27) NO.5 34-37.
28.萧嵘,王继成,孙正兴等.一种SVM增量学习算法-ISVM[J].软件学报,2001,12(12):1818-1824
29. Weston J.watkins C. Multi-class Support Machines[R]. Royal Holloway College, Tech Rep: CSD-TR-98-04, 1998.
30. Hsu C W,Lin C J.A Comparison of Methods for Multiclass Support Vector Machines [J].IEEE Trans. on Neural Networks,2002,13(2):415-425.
31. John C.Platt , Nello Cristianini, John Shawe-Taylor. Large Margin DAGs for Multiclass Classification[M].Advances in Neural Information Processing Systems12.MIT PRESS,2000.
32. Sungmoon C,Sang H O,Soo-Young L.Support Vector Machines with Binary Tree Architecturefor Multi-Class Classification[J].Neural Information Processing-Letters and Reviews,2004:2(3):47-51.
33.唐发明,王仲东,陈绵云.一种新的二叉树多类支持向量机算法[J],计算机工程与应用,2005.7:24-26.
34.马笑潇,黄席樾,柴毅.基于SVM的二叉树多类分类算法及其在故障诊断中的应用[J].控制与决策,2003:18(3) :272-276.
35.王建芬,曹元大.支持向量机在大类别数分类中的应用[J],北京理工大学学报,2001.21:225-227.
36. Brailovsky V.L.,et al.On Global,Local,Mixed and Neighborhood Kernels for Support VectorMachines[J]. Pattern Recognition Letters,1999,20:1183-1198.
37. Olivier Chapelle, etc. SVMs for Histogram-Based Image Classification[J]. IEEE Trans. On Neural Networks,1999,10(5):1055-1064.
38. Ofir Barzilay, etc. On Domain Knowledge and Feature Selection Using A Support Vector machine[J]. Pattern Recognition Letters,1999,20:475-484.
39. BCJC Burges,A J Smola.Advances in kernel methods-support vector learning[M].Cambridge, MA:MIT Press,1999.
40. E.Osuna,R.Freund, F.Girosit. Traaining Support Vector Machines: An Application to Face Detection[J]. Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1997,130-136.
41. T.Joachims.Transductive inference for Text Classification Using Support Vector Machines[R]. Presented at the Int.Conf.Machine Learning,Slovenia,1999.
42. Pontil M,Verri A. Support Vector Machines for 3D Object Recognition[J]. IEEE Trans. on Pattern Analysis and Machine Intelligence,1998,20(6):637-646.
43. Q.Zhao,J.Principe.Support Vector Machines for SAR Automatic Target Recognition[J].IEEE Trans.on Aerospace and Electronic Systems,2001,37(2):643-654.
44. K.I.Kim,K.Jung,et al.Support Vector Machines for Texture Classification[J].IEEE Trans.On Pattern Analysis and Machine Intelligence,2002,24(11):1542-1550.
45. Issam Ei-Naqa,Y-Y Yang,et al.A Support Vector Machine Approach for Detection of Microcalcifications[J]. IEEE Trans.On Medical Image,2002,21(12):1552-1563.
46. G.M.Fung and O.L.Mangasarian. Breast Tumor Susceptibility to Chemotherapy via Support Vector Machines[R].Data Mining Institute Technical Report 03-06,2003.
47. Claude E.Shannon. AMathematical Theory of Communication[J]. Bell System Tech. Journal,1948 , 27 :379-423.
48. M. F. Barnsley , A. D. Sloan.A Better Way to Compress Images[J].Byte Magazine. 1988 ,13 (1):215.
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