用于图像数据压缩的光学小波变换研究
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摘要
光学小波变换是近年来发展起来的实时处理信号的一种方法，它不仅为我们提供了一个抑制噪声、突出特征信息的手段，而且提供了一个实现多分辨率图像处理的有效途径。将它应用到图像数据压缩等领域具有广阔的应用前景。本论文系统地描述了小波变换的基本理论、基本性质，阐述了实现光学小波变换的两种方法：空间域法和频率域法。分析了采用4f光学系统在频率域对小波变换的光学实现。讨论了在实现光学小波变换的过程中，光学滤波器的选择，各项参数指标的确定。首先提出了在采用4f光学系统实现小波变换的过程中产生误差的分析方法以及今后改进的方向。
Optics wavelets transform is a real time digital process method which has developed in recent years. It can provide not only the means to suppress noises and extrude information, but also an effective approach to realize multi-distinguishing rate image process. If it would be applied in image and data compressing field, there will be a capacious applying prospect. This article systematically describes the basic principles and characters of wavelets transform, and expounds two means of realizing optics wavelets: space-field method, and frequency-field method. And the article analyses 4f optics system's application of optics realizing of optics wavelets, discusses the election of optics filter and the confirmations of parameters' targets, and brings forward firstly an error analyzing method in the course of realizing wavelets transform by 4f optics system and the improving orientation in the future.
Optics wavelets transform is a real time digital process method which has developed in recent years. It can provide not only the means to suppress noises and extrude information, but also an effective approach to realize multi-distinguishing rate image process. If it would be applied in image and data compressing field, there will be a capacious applying prospect. This article systematically describes the basic principles and characters of wavelets transform, and expounds two means of realizing optics wavelets: space-field method, and frequency-field method. And the article analyses 4f optics system's application of optics realizing of optics wavelets, discusses the election of optics filter and the confirmations of parameters' targets, and brings forward firstly an error analyzing method in the course of realizing wavelets transform by 4f optics system and the improving orientation in the future.
引文
[1] 宋菲君,S.Jutamulia.近代光学信息处理.北京大学出版社.2000
[2] Porter A B .On the diffraction theory of microscope vision. Phil May.1906,11(6):154-160
[3] Zenike F.Das phasenkontrastverfahren bei der mikroskopischen beobachtung,Z Techphys, 1935, 16: 545-656
[4] Vander Lugt A B.Signal detection by complex spatial filtering.IEEE Tran Inform Theory. 1964, IT-10:2
[5] Yu T F S.White-light processing technique for archival storage of colour film. Appl Opt. 1980, 19: 2457
[6] D Casasent.Optical and Fourier processor for product inspection . Opt,Eng.1988,Vol27,4:258
[7] Abdul Ahads,Awwal,Hua kuang Liu. Machine parts reconition using a trinary associative memory. Opt,Eng.1989,Vol28,5:537-543
[8] D Casasent .Optical processing techniques for advanced intelligent robot and computer vision. SPIE,1985 vol579:208-214
[9] J M Florence.Jiont transform correlator system using deformable mirror SLM. OPT, Lett. 1989, Vol14,341-343
[10] Don A Gregory ,James C Kirsch. Optical correlator:Optical computer that really works. SPIE. 1990,Vol1296:2-19
[11] F T S Yu.Comparison of detection efficiencies for Vander Lugt and joint transform correlator. Appl. Opt.1990,Vol29,No2:225
[12] B Javidi. Analysis of nonlinear optical correlation. SPIE,1988,Vol977:307-323
[13] 冉启文,潭立英.小波分析与分数傅立叶变换及应用.国防工业出版社.2002
[14] 邓东皋，彭立中.小波分析. 数学进展，1991，20（3）；294-310
[15] 刘贵忠，邸双亮.小波分析及其应用. 西安电子科技大学出版社,1993
[16] 秦前清，杨宗凯 .实用小波分析. 西安：西安电子科技大学出版社，1994
[17] 王建中 .小波理论及其在物理和工程中的应用. 数学进展，1992，21（3）：290-310
[18] 李世雄，刘家琦 .小波理论和反演数学基础. 北京：地址出版社，1994
[19] Gabor D. Theory of Communication .J. Inst.Elect.Eng., 1946,93(3)：429-457
[20] Morlet J. SeismicTomorrow: Interferometry and Quantum Mechanics. The 45th Annual International SEG meeting, New York,Oct ,15, 1972
[21] (美)崔锦泰著 .程正兴译. 小波分析导论. 西安交通大学出版社，1994
[22] A Grossmann,J Morlet.Ddcomposition of Hardy functions into square intergrable wavelets of
constant shape. SIAM Math Anal. 1984 15 723-736
[23] J M Combes,A Grossmann,Ph Tchamitchian.Proceedings of the International conference, Marseile, France 1987 Springer-verlag
[24] Y Meyer,Op'e rateurs,Paris:Hermann(1990)
[25] D J Burt,E H Adelson.IEEE Tran commum.1983,COM-31,532-542
[26] S Mallat. A Theroy of multiresolution signal decomposition:the waveletrepresentation .IEEE Trans pattern Anal Mach Intell. 1989,PAMI-31,674-693.
[27] A Grossmann, J Morlet, T Paul.Transforms associated to square inter geable group representations, Igeneralresults. J Math Phys.1985 26:2473-2479
[28] Y Meyer .Principe d'incertitude bases hibertiienes and algebras d'operation. Seminaire 1985 622
[29] P G Lemarie, Y Meyer.Ondeletters et baes Hibertiennes.Revista Mathematica Iberoamericana 1986 iy2(2)
[30] S G Mallat.Multifrequency channel decompositions of imagesans and wavelet models.IEEE Trans Acoust Speech sig .Proc 1989 Assp-37(12):2091-2110
[31] S G Mallat.Zero-corssings of a wavelet transform.IEEE Trans Inf Theroy 1991 37:1019-1033
[32] S G Mallat.A theory for multi-frequency signal decomposition. IEEE Trans pattern Anal Mach Intell, 1989,11:674-693
[33] I Daubechies.Orthonomal bases of compactly supported wavelets.Commun Pure Appl Math XLI 1988:909-996
[34] 胡昌华，张军波等.基于MATLAB的系统分析与设计-小波分析.西安电子科技大学出版社.1999
[35] 彭玉华.小波变换与工程应用. 科学出版社. 1999
[36] 杨福生.小波变换的工程分析与应用.科学出版社. 2000
[37] 徐长发，李国宽.实用小波分析.华中科技大学出版社.2001
[38] M Vrtterli,Cherler.IEEE Transaction on signal processing. 1992,40,9: 2207-2232
[39] M J Shensa.IEEE Transaction on signal processing,1991,40,10: 2461-2482
[40] Y L Sheng,Danny Roberge, Harold H Szu. Optical wavelet transform. Opt Eng. 1992, v31, 9:1840-1845
[41] Harold H Szu,Brian Telfe r,Adolf Lohmann.Causal analytical wavelet transform.Opt Eng. 1992, Vol31, 9:1825-1829
[42] Xiangyang Yang, Harold H Szu, Y L Sheng.Optical Haar wavelet transforms of binary images.Opt Eng.1992 ,Vol31,9:1846-1851
[43] Y L Sheng,Taiwei Lu,Danny Roberge,H John Caulfield.N4 Inplementation of a 2-D wavelet
transform. Opt Eng.1992 ,Vol31,9:1859-1864
[44] 马晶，谭立英等.光学小波滤波理论初探.中国激光.1999，4.Vol26,4: 343-346
[45] 苏显渝.信息光学.科学出版社.1999.
[46] 黄凯进，谢长生.空间调制器-实时光处理.激光与光电子进展.1998,4(总第338期): 8-13
[47] Mendlovic D,Ido Ouzeli Irena Kiruschev ,Achieved.Computer-Generated Multireference Match Filter and Dammmann Grating.Appl Opt.1995,Vol34,35:8213-8219
[48] Wang W L,Jin G F,Yan Y B,et al.Image Feature Extraction with Optical Haar Wavelet Transform. Opt Eng ,1995,Vol34,4:1238-1242
[49] Block P G,Rogers S K,Ruck D K. Optical Wavelet Transform from Computer-Generated Holography. Appl Opt.1994,Vol33,23:5275-5278
[50] Zhang Y,Kanterakis E K,Wang J M.Optoelectronic Wavelet Processors Based on Smart Interferometry.Appl Opt.1994,Vol33,23:5279-5286
[51] Meiyuan Wen,Shizhuo Yin,Purwosumarto Purwardi,Francis T S Yu.Wavelet matched filter using a photorefractive crystal. Optics Communication,1993:325-330
[52] Yan Zhang,Yak Li. Optical determination of Gabor coefficients of transient signal. Opt Lett. 1991, 16:1031-1033
[53] D Casasent,J-S Smokelin,A,Ye. Optical Gabor and wavelet transforms for scene analysis. Proc. SPIE 1702
[54] G Eichmann,C Lu,M Jankowski,R tolimieri. Shape representation by Gabor expansion inHybrid Image ang Singal processing Ⅱ.Proc SPIE1297. 1990,86-94
[55] 李在铭等.数字图像处理压缩与识别技术.电子科技大学出版社.2000
[56] H John Caulfield,Harold H Suz. Parallel discrete and continous wavelet transform. Opt Eng. 1992, Vol31,9:1835-1839
[57]（美）顾德门J W.傅立叶光学导论.科学出版社.1979
[58] W T Rhodes. One-dimensional to two-dimensional and two-dimensional to one-dimensional mapping in optical signal processing. Proc,SPIE128,1977,322-331
[59] W Stoner.Review of 1-D singal processing using the optical transfer function. Proc SPIE634, 1986,64-79
[60] P J Burt,E H Adelson. The Laplacian pyramid as a compact image code. IEEE Trans Commun 1983, COM-31:532-540
[61] 李骏.子波变换及其光学实现方法研究. 长春光机所博士学位论文，1995.5
[62] S Mallet. A Theroy for multiresolution of signal decomposition:wavelet representation. IEEE Trans.Pattern Anal.Machine Intell.1989,31：674
[63] Y Zhang ,Y Li. Optical determination of Gabor coefficients of transient signals Opt. Lett. 1991,
16:1031-1033
[64] M Conner,L Li. Optical generation of the wigner distribution of 2-D real signals. Appl. Opt. 1986, 24,3825-3831
[65] B Friedlaner,B Porat. Detection of transient signal by the Gabor representation. IEEE Trans. Acoust.Speech sig.proc.1989.37:169-180
[66] Harold H Suz,H John Caulifield. Wavwlet Transform. Opt.Eng. 1992, Vol31,9: 1823-1823
[67] H John Caulifield, Harold H Suz. Parallel discrete and continuous wavelet transforms. Opt. Eng. 1992, Vol31,9:1835-1839
[68] A Haar,Ph.D.dissertation,appendix(1910)
[69] A Haar.Zur theorie der orthogonalen funktionen-systeme. Math.Annal.1910,69:331-371
[70] 华家宁，陈家璧.光学小波变换初探. 南京师大学报.1994,Vol17,4:34-37
[71] 金国蕃, 王文陆等. 光学小波变换（1）基本理论. 光电子·激光. 1994，8.Vol5,4: 193-200
[72] 王文陆,金国蕃等. 光学小波变换（2）实验结构及技术. 光电子·激光. 1994，10. Vol5, 5:268-272
[73] 王文陆,严瑛白等. 光学小波变换（3）应用.光电子·激光. 1994，12.Vol5,6：331-339
[74] 聂守罕，杨罕等.子波变换在光信息处理方面的应用.应用光学.1994,8.Vol15,4：41-44
[75] 倪明，蒋志平等.一种光学小波变换的改进.中国激光.1997,3.Vol24,3：231-236
[76] 陈鹤鸣等.用计算全息制作改进的Mexican-hat子波匹配滤波器实现二维光学子波变换. 中国激光.1999,5Vol26,5:421-424
[77] 朱建华.光学小波变换中尺度因子的极限.中国激光.2000,11.Vol27,11.1025-1028
[78] 王取泉，李琳等.改进4f傅立叶光学系统实现平面分形的频谱放大和小波变换.光学学报. 2000, 2.Vol20,2：219-223
[79] 王仲民岳宏.二维小波变换的光学实现.天津职业技术师范学院学报.2001,9.Vol11,3：14-16
[80] 田逢春：小波变换实现图像数据压缩时边界问题及其线性相位有限长脉冲响应滤波器的逼近，重庆大学博士学位论文，1996.5
[2] Porter A B .On the diffraction theory of microscope vision. Phil May.1906,11(6):154-160
[3] Zenike F.Das phasenkontrastverfahren bei der mikroskopischen beobachtung,Z Techphys, 1935, 16: 545-656
[4] Vander Lugt A B.Signal detection by complex spatial filtering.IEEE Tran Inform Theory. 1964, IT-10:2
[5] Yu T F S.White-light processing technique for archival storage of colour film. Appl Opt. 1980, 19: 2457
[6] D Casasent.Optical and Fourier processor for product inspection . Opt,Eng.1988,Vol27,4:258
[7] Abdul Ahads,Awwal,Hua kuang Liu. Machine parts reconition using a trinary associative memory. Opt,Eng.1989,Vol28,5:537-543
[8] D Casasent .Optical processing techniques for advanced intelligent robot and computer vision. SPIE,1985 vol579:208-214
[9] J M Florence.Jiont transform correlator system using deformable mirror SLM. OPT, Lett. 1989, Vol14,341-343
[10] Don A Gregory ,James C Kirsch. Optical correlator:Optical computer that really works. SPIE. 1990,Vol1296:2-19
[11] F T S Yu.Comparison of detection efficiencies for Vander Lugt and joint transform correlator. Appl. Opt.1990,Vol29,No2:225
[12] B Javidi. Analysis of nonlinear optical correlation. SPIE,1988,Vol977:307-323
[13] 冉启文,潭立英.小波分析与分数傅立叶变换及应用.国防工业出版社.2002
[14] 邓东皋，彭立中.小波分析. 数学进展，1991，20（3）；294-310
[15] 刘贵忠，邸双亮.小波分析及其应用. 西安电子科技大学出版社,1993
[16] 秦前清，杨宗凯 .实用小波分析. 西安：西安电子科技大学出版社，1994
[17] 王建中 .小波理论及其在物理和工程中的应用. 数学进展，1992，21（3）：290-310
[18] 李世雄，刘家琦 .小波理论和反演数学基础. 北京：地址出版社，1994
[19] Gabor D. Theory of Communication .J. Inst.Elect.Eng., 1946,93(3)：429-457
[20] Morlet J. SeismicTomorrow: Interferometry and Quantum Mechanics. The 45th Annual International SEG meeting, New York,Oct ,15, 1972
[21] (美)崔锦泰著 .程正兴译. 小波分析导论. 西安交通大学出版社，1994
[22] A Grossmann,J Morlet.Ddcomposition of Hardy functions into square intergrable wavelets of
constant shape. SIAM Math Anal. 1984 15 723-736
[23] J M Combes,A Grossmann,Ph Tchamitchian.Proceedings of the International conference, Marseile, France 1987 Springer-verlag
[24] Y Meyer,Op'e rateurs,Paris:Hermann(1990)
[25] D J Burt,E H Adelson.IEEE Tran commum.1983,COM-31,532-542
[26] S Mallat. A Theroy of multiresolution signal decomposition:the waveletrepresentation .IEEE Trans pattern Anal Mach Intell. 1989,PAMI-31,674-693.
[27] A Grossmann, J Morlet, T Paul.Transforms associated to square inter geable group representations, Igeneralresults. J Math Phys.1985 26:2473-2479
[28] Y Meyer .Principe d'incertitude bases hibertiienes and algebras d'operation. Seminaire 1985 622
[29] P G Lemarie, Y Meyer.Ondeletters et baes Hibertiennes.Revista Mathematica Iberoamericana 1986 iy2(2)
[30] S G Mallat.Multifrequency channel decompositions of imagesans and wavelet models.IEEE Trans Acoust Speech sig .Proc 1989 Assp-37(12):2091-2110
[31] S G Mallat.Zero-corssings of a wavelet transform.IEEE Trans Inf Theroy 1991 37:1019-1033
[32] S G Mallat.A theory for multi-frequency signal decomposition. IEEE Trans pattern Anal Mach Intell, 1989,11:674-693
[33] I Daubechies.Orthonomal bases of compactly supported wavelets.Commun Pure Appl Math XLI 1988:909-996
[34] 胡昌华，张军波等.基于MATLAB的系统分析与设计-小波分析.西安电子科技大学出版社.1999
[35] 彭玉华.小波变换与工程应用. 科学出版社. 1999
[36] 杨福生.小波变换的工程分析与应用.科学出版社. 2000
[37] 徐长发，李国宽.实用小波分析.华中科技大学出版社.2001
[38] M Vrtterli,Cherler.IEEE Transaction on signal processing. 1992,40,9: 2207-2232
[39] M J Shensa.IEEE Transaction on signal processing,1991,40,10: 2461-2482
[40] Y L Sheng,Danny Roberge, Harold H Szu. Optical wavelet transform. Opt Eng. 1992, v31, 9:1840-1845
[41] Harold H Szu,Brian Telfe r,Adolf Lohmann.Causal analytical wavelet transform.Opt Eng. 1992, Vol31, 9:1825-1829
[42] Xiangyang Yang, Harold H Szu, Y L Sheng.Optical Haar wavelet transforms of binary images.Opt Eng.1992 ,Vol31,9:1846-1851
[43] Y L Sheng,Taiwei Lu,Danny Roberge,H John Caulfield.N4 Inplementation of a 2-D wavelet
transform. Opt Eng.1992 ,Vol31,9:1859-1864
[44] 马晶，谭立英等.光学小波滤波理论初探.中国激光.1999，4.Vol26,4: 343-346
[45] 苏显渝.信息光学.科学出版社.1999.
[46] 黄凯进，谢长生.空间调制器-实时光处理.激光与光电子进展.1998,4(总第338期): 8-13
[47] Mendlovic D,Ido Ouzeli Irena Kiruschev ,Achieved.Computer-Generated Multireference Match Filter and Dammmann Grating.Appl Opt.1995,Vol34,35:8213-8219
[48] Wang W L,Jin G F,Yan Y B,et al.Image Feature Extraction with Optical Haar Wavelet Transform. Opt Eng ,1995,Vol34,4:1238-1242
[49] Block P G,Rogers S K,Ruck D K. Optical Wavelet Transform from Computer-Generated Holography. Appl Opt.1994,Vol33,23:5275-5278
[50] Zhang Y,Kanterakis E K,Wang J M.Optoelectronic Wavelet Processors Based on Smart Interferometry.Appl Opt.1994,Vol33,23:5279-5286
[51] Meiyuan Wen,Shizhuo Yin,Purwosumarto Purwardi,Francis T S Yu.Wavelet matched filter using a photorefractive crystal. Optics Communication,1993:325-330
[52] Yan Zhang,Yak Li. Optical determination of Gabor coefficients of transient signal. Opt Lett. 1991, 16:1031-1033
[53] D Casasent,J-S Smokelin,A,Ye. Optical Gabor and wavelet transforms for scene analysis. Proc. SPIE 1702
[54] G Eichmann,C Lu,M Jankowski,R tolimieri. Shape representation by Gabor expansion inHybrid Image ang Singal processing Ⅱ.Proc SPIE1297. 1990,86-94
[55] 李在铭等.数字图像处理压缩与识别技术.电子科技大学出版社.2000
[56] H John Caulfield,Harold H Suz. Parallel discrete and continous wavelet transform. Opt Eng. 1992, Vol31,9:1835-1839
[57]（美）顾德门J W.傅立叶光学导论.科学出版社.1979
[58] W T Rhodes. One-dimensional to two-dimensional and two-dimensional to one-dimensional mapping in optical signal processing. Proc,SPIE128,1977,322-331
[59] W Stoner.Review of 1-D singal processing using the optical transfer function. Proc SPIE634, 1986,64-79
[60] P J Burt,E H Adelson. The Laplacian pyramid as a compact image code. IEEE Trans Commun 1983, COM-31:532-540
[61] 李骏.子波变换及其光学实现方法研究. 长春光机所博士学位论文，1995.5
[62] S Mallet. A Theroy for multiresolution of signal decomposition:wavelet representation. IEEE Trans.Pattern Anal.Machine Intell.1989,31：674
[63] Y Zhang ,Y Li. Optical determination of Gabor coefficients of transient signals Opt. Lett. 1991,
16:1031-1033
[64] M Conner,L Li. Optical generation of the wigner distribution of 2-D real signals. Appl. Opt. 1986, 24,3825-3831
[65] B Friedlaner,B Porat. Detection of transient signal by the Gabor representation. IEEE Trans. Acoust.Speech sig.proc.1989.37:169-180
[66] Harold H Suz,H John Caulifield. Wavwlet Transform. Opt.Eng. 1992, Vol31,9: 1823-1823
[67] H John Caulifield, Harold H Suz. Parallel discrete and continuous wavelet transforms. Opt. Eng. 1992, Vol31,9:1835-1839
[68] A Haar,Ph.D.dissertation,appendix(1910)
[69] A Haar.Zur theorie der orthogonalen funktionen-systeme. Math.Annal.1910,69:331-371
[70] 华家宁，陈家璧.光学小波变换初探. 南京师大学报.1994,Vol17,4:34-37
[71] 金国蕃, 王文陆等. 光学小波变换（1）基本理论. 光电子·激光. 1994，8.Vol5,4: 193-200
[72] 王文陆,金国蕃等. 光学小波变换（2）实验结构及技术. 光电子·激光. 1994，10. Vol5, 5:268-272
[73] 王文陆,严瑛白等. 光学小波变换（3）应用.光电子·激光. 1994，12.Vol5,6：331-339
[74] 聂守罕，杨罕等.子波变换在光信息处理方面的应用.应用光学.1994,8.Vol15,4：41-44
[75] 倪明，蒋志平等.一种光学小波变换的改进.中国激光.1997,3.Vol24,3：231-236
[76] 陈鹤鸣等.用计算全息制作改进的Mexican-hat子波匹配滤波器实现二维光学子波变换. 中国激光.1999,5Vol26,5:421-424
[77] 朱建华.光学小波变换中尺度因子的极限.中国激光.2000,11.Vol27,11.1025-1028
[78] 王取泉，李琳等.改进4f傅立叶光学系统实现平面分形的频谱放大和小波变换.光学学报. 2000, 2.Vol20,2：219-223
[79] 王仲民岳宏.二维小波变换的光学实现.天津职业技术师范学院学报.2001,9.Vol11,3：14-16
[80] 田逢春：小波变换实现图像数据压缩时边界问题及其线性相位有限长脉冲响应滤波器的逼近，重庆大学博士学位论文，1996.5