基于光学小波变换的图像压缩编码
摘要
光学小波变换是光学信息处理与小波理论的结合,同时汇集了光学技术和小波变换的诸多优点,有利于信息处理的高速化。将光学小波变换技术应用到图像数据压缩是前沿课题之一,实现基于光学信息处理的图像压缩对于图像信息的存储和传输有重要的理论意义和现实价值。本论文介绍小波基本理论,研究小波变换用于图像数据压缩时各种因素对信息熵的影响,分析小波图像数据压缩方法和光学小波变换系统的特点,提出了基于光学小波变换的近无损和有损压缩方法。
研究图像小波变换对信息熵的影响。通过大量仿真实验,研究图像包含频率成份、小波分解级数、小波基函数等对小波分解后的小波系数信息熵的影响,实验结果表明,要想得到小波分解后较小的信息熵,一般应采用3级小波变换,采用双正交小波分解的效果优于其他小波,小波基的消失矩较高较有利等,为小波变换应用于图像数据压缩提供了依据。
阐述光学小波变换对小波基的要求,分析小波图像数据压缩编码方法。综合以上实验结论和小波变换用于图像压缩时对小波基的要求,阐述适合光学系统的小波基选择。在分析传统静态图像压缩算法的基础上,介绍图像小波分解的特点和编码发展,研究目前较常用的几种针对小波系数特点的嵌入式编码算法,并比较各方法的优缺点。
实现基于光学小波变换的图像数据压缩。分析光学小波变换系统和光学小波变换系数特点,基于此,对相关量化编码方案进行仿真实验,根据理论分析和实验结果选定带死区的均匀量化、小波EBCOT编码对光学小波系数进行编码。实验结果证实了方法的有效性。
分析光学系统对量化编码噪声的容许程度,实验结果表明只要在量化、压缩过程中产生的噪声低于系统本身噪声,对解码重建图像质量就没有很大影响,由此提出光学系统的近无损压缩方法。实验结果表明,近无损压缩重建图像与经光学小波变换直接重建图像相比,PSNR仅有0.1dB的差异,视觉上没有明显差异。实验结果验证了方法的正确性。
Optical wavelet transform is the combination of optical information processing and wavelet theory. It integrates many advantages of optical science and wavelet transform while providing advantageous basis for high-speed information processing. Optical wavelet transform for image data compression is one of the frontiers. Realizing image data compression on optical system will have important theoretic meaning and practical value for images’storage and transmission. The fundamental theory of wavelet was described and the effect on entropy for several factors in wavelet transform was studied in this dissertation. Then the methods of image compression after wavelet transform and the optical system’s characteristics were analyzed in detail. And nearly lossless compression and lossy compression of optical wavelet coefficients were proposed.
The variation of image entropy before and after wavelet decomposition, the optimal number of wavelet decomposition layer, the effect on the entropy by wavelet basis and image’s frequency components etc. were studied by a large number of simulation experiments. It is verified that to get the minimal entropy, generally a three-layer decomposition should be adapted rather than higher orders. The result by biorthogonal wavelet decomposition is better than by orthogonal one. And it‘s true that the higher of the vanishing moment, the better the result.
The requirement for wavelet bases in optical wavelet transform is introduced and the methods of image compression with wavelet transform were analyzed in detail. Considering the above experimental results and the requirements of wavelet bases in image compression, the choice of appropriate wavelet bases for the optical system was described. Based on traditional static image compression algorithms, the characteristics of wavelet coefficients and the development of coding methods were introduced. Especially the commonly used embedded coding algorithms were analyzed in detail. And the advantages and disadvantages of these methods were compared.
Image data compression based on optical wavelet transform was achieved here. First, characteristics of optical system and optical wavelet transform coefficients were analyzed. According to these characteristics, simulation was did on several quantified and coding methods. Based on the results, the dead zone uniform quantization and EBCOT were chose. And the corresponding experiments confirmed the validity of these methods.
In addition, from analyzing the endurance to quantity noise of optical system, an important conclusion was achieved which sparked the ideas of nearly lossless compression. It is described as: so long as the noise caused by quantizing and coding is less than the noise produced by the system itself, the quality of the decoding image would not be affected greatly. Experimental results showed that, compared with the image reconstructed directly, the nearly lossless reconstructed image’s PSNR was only 0.1dB lower, and there was no significant difference visually.
研究图像小波变换对信息熵的影响。通过大量仿真实验,研究图像包含频率成份、小波分解级数、小波基函数等对小波分解后的小波系数信息熵的影响,实验结果表明,要想得到小波分解后较小的信息熵,一般应采用3级小波变换,采用双正交小波分解的效果优于其他小波,小波基的消失矩较高较有利等,为小波变换应用于图像数据压缩提供了依据。
阐述光学小波变换对小波基的要求,分析小波图像数据压缩编码方法。综合以上实验结论和小波变换用于图像压缩时对小波基的要求,阐述适合光学系统的小波基选择。在分析传统静态图像压缩算法的基础上,介绍图像小波分解的特点和编码发展,研究目前较常用的几种针对小波系数特点的嵌入式编码算法,并比较各方法的优缺点。
实现基于光学小波变换的图像数据压缩。分析光学小波变换系统和光学小波变换系数特点,基于此,对相关量化编码方案进行仿真实验,根据理论分析和实验结果选定带死区的均匀量化、小波EBCOT编码对光学小波系数进行编码。实验结果证实了方法的有效性。
分析光学系统对量化编码噪声的容许程度,实验结果表明只要在量化、压缩过程中产生的噪声低于系统本身噪声,对解码重建图像质量就没有很大影响,由此提出光学系统的近无损压缩方法。实验结果表明,近无损压缩重建图像与经光学小波变换直接重建图像相比,PSNR仅有0.1dB的差异,视觉上没有明显差异。实验结果验证了方法的正确性。
Optical wavelet transform is the combination of optical information processing and wavelet theory. It integrates many advantages of optical science and wavelet transform while providing advantageous basis for high-speed information processing. Optical wavelet transform for image data compression is one of the frontiers. Realizing image data compression on optical system will have important theoretic meaning and practical value for images’storage and transmission. The fundamental theory of wavelet was described and the effect on entropy for several factors in wavelet transform was studied in this dissertation. Then the methods of image compression after wavelet transform and the optical system’s characteristics were analyzed in detail. And nearly lossless compression and lossy compression of optical wavelet coefficients were proposed.
The variation of image entropy before and after wavelet decomposition, the optimal number of wavelet decomposition layer, the effect on the entropy by wavelet basis and image’s frequency components etc. were studied by a large number of simulation experiments. It is verified that to get the minimal entropy, generally a three-layer decomposition should be adapted rather than higher orders. The result by biorthogonal wavelet decomposition is better than by orthogonal one. And it‘s true that the higher of the vanishing moment, the better the result.
The requirement for wavelet bases in optical wavelet transform is introduced and the methods of image compression with wavelet transform were analyzed in detail. Considering the above experimental results and the requirements of wavelet bases in image compression, the choice of appropriate wavelet bases for the optical system was described. Based on traditional static image compression algorithms, the characteristics of wavelet coefficients and the development of coding methods were introduced. Especially the commonly used embedded coding algorithms were analyzed in detail. And the advantages and disadvantages of these methods were compared.
Image data compression based on optical wavelet transform was achieved here. First, characteristics of optical system and optical wavelet transform coefficients were analyzed. According to these characteristics, simulation was did on several quantified and coding methods. Based on the results, the dead zone uniform quantization and EBCOT were chose. And the corresponding experiments confirmed the validity of these methods.
In addition, from analyzing the endurance to quantity noise of optical system, an important conclusion was achieved which sparked the ideas of nearly lossless compression. It is described as: so long as the noise caused by quantizing and coding is less than the noise produced by the system itself, the quality of the decoding image would not be affected greatly. Experimental results showed that, compared with the image reconstructed directly, the nearly lossless reconstructed image’s PSNR was only 0.1dB lower, and there was no significant difference visually.
引文
[1]郑光昭.光信息科学技术[M].电子工业出版社, 2002.10.
[2]王仕璠.信息光学理论与应用[M].北京邮电大学出版社, 2003.12.
[3]清华大学光学仪器教研组.信息光学基础[M].机械工业出版社, 1985.12.
[4] A.Huang. Arichitectural consideration involved in the design of an optical digital computer[J]. Proceeding of the IEEE, 1984, 72 (7): 780-786.
[5] Woods J W, O’Neil S D. Subband coding of images [J]. IEEE Trans. On Acoustics, Speech, and Signal Processing, 1986, 34(5):1278-1288.
[6] Mallat S G. Multifrequency Channel Decomposition of Images and Wavelet Models [J]. IEEE Trans. On Acoustics, Speech and Signal Processing, 1989, 37 (12):2091~2110.
[7] Vetterli M. Filter banks allowing perfect reconstruction [J]. Signal Process., 1986, 10:219-244
[8] Sweldens W. The lifting scheme: a new philosophy in biorthogonal wavelet constructions [J]. Proc. SPIE,1995,2569:68-79.
[9] Lewis A S, Knowles G. Image compression using 2-D wavelet transform [J]. IEEE Trans. On Image Processing, 1992,1(2).
[10] Shapiro JM. Embedded image coding using zero tree of wavelet coefficients [J]. IEEE Transactions on Signal Processing, 1993.41 ( 12 ) :3445—3462.
[11] A. Said and W. Pearlman, A new, fast and efficient image codec based on set partitioning in hierarchical trees[J], IEEE Trans. Circuits and Systems for Video Technology, 1996.6(3):243-250.
[12] A. Islam and W. A. Pearlman, An Embedded and Efficient Low-Complexity Hierarchical Image Coder[J], Visual Communications and Image Processing’99, Proceedings of SPIE , Jan. 1999.3653:294-305.
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[18] E. Freysz, B. Pouligny, F. Argoul, et al.. Optical wavelet transform of fractal aggregates[J]. Phys. Rev. Lett., 1990, 64 (7): 745-748.
[19]陈艳燕.小波变换在光学处理中的应用[M].华中师范大学硕士论文, 2001.
[20] Yan.Zhang, Yao Li. Optical determination of Gabor coefficients of transient signals[J]. Opt. Lett., 1991, 16 (13): 1031-1033.
[21] C. Hirliman, J. F. Morhange. Wavelet analysis of short light pulses. Applied Optics[J], 1992, 31(17): 3263-3266.
[22] Y. Sheng, D. Roberge, H. Szu, T. Lu. Optical wavelet matched filters for shift-invariant pattern recognition[J]. Opt. Lett., 1993, 18 (4): 299-301.
[23] M. O. Freeman. Wavelets: signal representations with important advantages[J]. Opt. Photon, 1993, 4 (8): 8-14.
[24] D. Mendlovic, N. Konforti. Optical realization of the wavelet transform for two-dimensional objects[J]. Appl.Opt., 1993, 32 (32): 6542-6546.
[25]王文陆,严瑛白,金国藩,邬敏贤.光学子波变换(1):基本理论[J].光电子·激光, 1994. 5(4): 193-200.
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[29]赵维义,宋菲君,俞蕾.光学小波变换[J].物理, 2000, 3 (29): 162-168.
[30]聂守平,杨罕,李爱民.一种新颖的光信息处理方法--子波变换[J].南京理工大学学报, 1995, 19 (1): 13-16.
[31]程正兴.小波分析算法与应用[M].西安:西安交通大学出版社,2003.
[32] Mallat S G. Multifrequency Channel Decomposition of Images and Wavelet Models [J]. IEEE Trans. On Acoustics, Speech and Signal Processing, 1989, 37 (12):2091~2110.
[33] Mallat S G. A Theory for Multiresolution Signal Decomposition: the Wavelet Representation[J]. IEEE Trans. On Pattern Recognition and Machine Intelligence, 1989,11(7): 674~693.
[34] Vetterli M. and Herley C. Wavelet and filter banks[J]: Theory and design. IEEE Trans. Acoust. Speech Signal Proc., 1992, 40(9):2207-2232.
[35] Coifman R.R. and Wickerhauser M.V. Entropy based algorithms for best basis selection[J].IEEE Trans.Inform. Theory,1992.2, 38(2):713-718.
[36] Sweldens W. The lifting scheme: construction of second generation wavelets[J]. SIAM J. Math.Anal. , 1997,29(2):511-546.
[37]孙延奎.小波分析及其应用[M].机械工业出版社, 2005.3.
[38]秦前清,杨宗凯.实用小波分析[M].西安电子科技大学出版社, 1995.
[39] I. Daubechies [著].李建平,杨万年[译].小波十讲[M].国防工业出版社, 2004.5.
[40]冯象初,甘小冰,宋国乡.数值泛函与小波理论[M].西安电子科技大学出版社,2003.
[41] Rui CHC, Mariaa AGVF, Arie EK, et al. Wavelet and entropy analysis combination to evaluate diffusion and correlation behaviors [C]. In: Proceedings of X Brazilian Symposium on Computer Graphics and Image, Campos do Jordao, Brazil, October 14-17, 1997. USA: Technical Communication Services, 1997: 192-125.
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[46]韩亮,田逢春,徐鑫,李立. Mallat算法的光学实现方法[M].光学精密工程,2007年12月录用.
[47]田逢春,韩亮,王宇,徐鑫.空频域量化误差最小的光学小波滤波器设计[J].光电工程,2007年12月录用.
[48]张旭东,卢国栋,冯健.图像压缩编码基础和小波压缩技术-原理、算法和标准[M].清华大学出版社, 2004.3.
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[2]王仕璠.信息光学理论与应用[M].北京邮电大学出版社, 2003.12.
[3]清华大学光学仪器教研组.信息光学基础[M].机械工业出版社, 1985.12.
[4] A.Huang. Arichitectural consideration involved in the design of an optical digital computer[J]. Proceeding of the IEEE, 1984, 72 (7): 780-786.
[5] Woods J W, O’Neil S D. Subband coding of images [J]. IEEE Trans. On Acoustics, Speech, and Signal Processing, 1986, 34(5):1278-1288.
[6] Mallat S G. Multifrequency Channel Decomposition of Images and Wavelet Models [J]. IEEE Trans. On Acoustics, Speech and Signal Processing, 1989, 37 (12):2091~2110.
[7] Vetterli M. Filter banks allowing perfect reconstruction [J]. Signal Process., 1986, 10:219-244
[8] Sweldens W. The lifting scheme: a new philosophy in biorthogonal wavelet constructions [J]. Proc. SPIE,1995,2569:68-79.
[9] Lewis A S, Knowles G. Image compression using 2-D wavelet transform [J]. IEEE Trans. On Image Processing, 1992,1(2).
[10] Shapiro JM. Embedded image coding using zero tree of wavelet coefficients [J]. IEEE Transactions on Signal Processing, 1993.41 ( 12 ) :3445—3462.
[11] A. Said and W. Pearlman, A new, fast and efficient image codec based on set partitioning in hierarchical trees[J], IEEE Trans. Circuits and Systems for Video Technology, 1996.6(3):243-250.
[12] A. Islam and W. A. Pearlman, An Embedded and Efficient Low-Complexity Hierarchical Image Coder[J], Visual Communications and Image Processing’99, Proceedings of SPIE , Jan. 1999.3653:294-305.
[13]小野定康,铃木纯司. JPEG2000技术[M].科学出版社, 2004.4.
[14] S. David. Taubman, W. Michael. Marcellin. JPEG2000图像压缩基础、标准和实践[M].电子工业出版社, 2004.4.
[15]赵建林.高等光学[M].西北工业大学出版社, 1999.
[16] D.G.Feitelson. Optical computing-a survey for computer scientists[J]. the MIT Press, 1988.
[17] A.W.Lohman. what classical optics can do for digital optical computer[J]. Applied Optics, 1986, 25 (10): 1543-1549.
[18] E. Freysz, B. Pouligny, F. Argoul, et al.. Optical wavelet transform of fractal aggregates[J]. Phys. Rev. Lett., 1990, 64 (7): 745-748.
[19]陈艳燕.小波变换在光学处理中的应用[M].华中师范大学硕士论文, 2001.
[20] Yan.Zhang, Yao Li. Optical determination of Gabor coefficients of transient signals[J]. Opt. Lett., 1991, 16 (13): 1031-1033.
[21] C. Hirliman, J. F. Morhange. Wavelet analysis of short light pulses. Applied Optics[J], 1992, 31(17): 3263-3266.
[22] Y. Sheng, D. Roberge, H. Szu, T. Lu. Optical wavelet matched filters for shift-invariant pattern recognition[J]. Opt. Lett., 1993, 18 (4): 299-301.
[23] M. O. Freeman. Wavelets: signal representations with important advantages[J]. Opt. Photon, 1993, 4 (8): 8-14.
[24] D. Mendlovic, N. Konforti. Optical realization of the wavelet transform for two-dimensional objects[J]. Appl.Opt., 1993, 32 (32): 6542-6546.
[25]王文陆,严瑛白,金国藩,邬敏贤.光学子波变换(1):基本理论[J].光电子·激光, 1994. 5(4): 193-200.
[26]王文陆,严瑛白,金国藩,邬敏贤.光学子波变换(2):实验结构及技术[J].光电子·激光, 1994, 5 (5): 268-272.
[27]王文陆,严瑛白,金国藩,邬敏贤.光学子波变换(3):应用[J].光电子·激光, 1994, 5 (6): 331-339.
[28]华家宁,陈家壁.光学小波变换初探[J].南京师大学报(自然科学版), 1994, 17 (4): 31-37.
[29]赵维义,宋菲君,俞蕾.光学小波变换[J].物理, 2000, 3 (29): 162-168.
[30]聂守平,杨罕,李爱民.一种新颖的光信息处理方法--子波变换[J].南京理工大学学报, 1995, 19 (1): 13-16.
[31]程正兴.小波分析算法与应用[M].西安:西安交通大学出版社,2003.
[32] Mallat S G. Multifrequency Channel Decomposition of Images and Wavelet Models [J]. IEEE Trans. On Acoustics, Speech and Signal Processing, 1989, 37 (12):2091~2110.
[33] Mallat S G. A Theory for Multiresolution Signal Decomposition: the Wavelet Representation[J]. IEEE Trans. On Pattern Recognition and Machine Intelligence, 1989,11(7): 674~693.
[34] Vetterli M. and Herley C. Wavelet and filter banks[J]: Theory and design. IEEE Trans. Acoust. Speech Signal Proc., 1992, 40(9):2207-2232.
[35] Coifman R.R. and Wickerhauser M.V. Entropy based algorithms for best basis selection[J].IEEE Trans.Inform. Theory,1992.2, 38(2):713-718.
[36] Sweldens W. The lifting scheme: construction of second generation wavelets[J]. SIAM J. Math.Anal. , 1997,29(2):511-546.
[37]孙延奎.小波分析及其应用[M].机械工业出版社, 2005.3.
[38]秦前清,杨宗凯.实用小波分析[M].西安电子科技大学出版社, 1995.
[39] I. Daubechies [著].李建平,杨万年[译].小波十讲[M].国防工业出版社, 2004.5.
[40]冯象初,甘小冰,宋国乡.数值泛函与小波理论[M].西安电子科技大学出版社,2003.
[41] Rui CHC, Mariaa AGVF, Arie EK, et al. Wavelet and entropy analysis combination to evaluate diffusion and correlation behaviors [C]. In: Proceedings of X Brazilian Symposium on Computer Graphics and Image, Campos do Jordao, Brazil, October 14-17, 1997. USA: Technical Communication Services, 1997: 192-125.
[42]曹雪虹,张宗橙.信息理论与编码[M].北京:清华大学出版社, 2004.
[43] Department of Electrical Engineering. The USC-SIPI Image Database [DB/OL]. USA: University of Southern California. [cited 2006-03-05]. http://sipi.usc.edu/database
[44]龚声蓉,刘纯平,王强.数字图像处理与分析[M].清华大学出版社,2006.
[45]孙即祥等.图像压缩与投影重建[M].北京科学出版社,2005.
[46]韩亮,田逢春,徐鑫,李立. Mallat算法的光学实现方法[M].光学精密工程,2007年12月录用.
[47]田逢春,韩亮,王宇,徐鑫.空频域量化误差最小的光学小波滤波器设计[J].光电工程,2007年12月录用.
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