摘要
多组分重叠信号的解析一直是分析化学研究领域中具有挑战性的问题，免疫算法和小波变换是两种解析多组分重叠信号的有效工具。本文首先简要介绍了免疫算法和小波变换的基本原理和基本算法，并综述了近年来在分析化学领域中的应用。然后对免疫算法和小波变换在解析重叠信号方面的应用进行了深入研究，完成了以下几个方面的工作内容：基于小波压缩和免疫算法，提出了一种用于解析多组分重叠二维色谱信号的快速算法。通过对多组分二维重叠色谱信号的解析和定量计算，结果表明小波压缩—免疫算法的计算速度快、定量准确，是解析多组分二维重叠色谱的有效方法，可作为免疫—遗传算法的快速预处理的候选方法。
基于免疫算法的基本原理，提出了一种自适应免疫算法。通过建立标准峰的数据库，从数据库中自适应地产生用于混合物信号解析的标样信息。通过计算混合物信号与标样信号之间的相关系数和采用优化策略，使算法变得更加智能，算法的效率得到明显提高。将其应用于4组分NMR谱和9组分NMR谱的解析，结果表明该方法是一种有效的自适应免疫算法，与免疫遗传算法相比计算速度更快，解析结果更精确。
为了对多组分重叠色谱信号进行定量分析，提出了将变形算法与小波变换平滑、三次样条插值及一个新的确定最佳数据点数的标准相结合的改进算法。使用改进的算法，可以有效抑制由于变形产生的振荡。通过对模拟信号的解析，结果表明改进的算法具有更强的解析能力，降低了对重叠信号分离度、噪声水平及峰形方面的限制要求。通过对实验色谱信号的解析，进一步证明了其优点。研究结果表明，改进的变形算法与原来的算法相比在多组分重叠色谱定量解析方面更具有实用性。
本文还对独立成分分析法(ICA)在多组分重叠NMR解析中的应用进行了研究。由于NMR信号与ICA假设条件之间的不一致，在某些情况下使用ICA不能直接得到正确的解析结果。因此，提出了一种对ICA的计算结果进行再旋转的方法用来修正ICA的计算结果。通过对模拟10组分混合物NMR谱和2组分
Resolution of multicomponent overlapping signals is one of the challenging tasks in analytical chemistry studies. Both immune algorithm and wavelet transform are effective tools for resolution of multicomponent overlapping signals. In this dissertation, at first, the theory and algorithm of immune algorithm and wavelet transform are introduced and the applications of them in analytical chemistry are reviewed. Then, with the aim to develop new tools for resolution of overlapping analytical signals, the following works are carried out:
Based on the wavelet compression and immune algorithm, a fast algorithm for resolution of 2-D multicomponent overlapping chromatogram is proposed. By application of the method in resolution and quantitative determination of multicomponent 2-D overlapping chromatograms, it is demonstrated that this method is fast in calculation speed and accurate in quantitative calculation. Therefore, the proposed algorithm may be an alternative effective method for resolution of multicomponent 2-D overlapping chromatogram.
Based on the immune algorithm, an adaptive immune algorithm is proposed. With the establishment of the database of the standards peaks, the standard information is adaptively generated from the database for the resolution of the mixture sample. With the adoption of the correlation coefficient between mixture signal and standard signals and the optimal strategy, the algorithm is much more intelligentized and the efficiency of the algorithm is improved obviously. From the resolution results of a four-component NMR spectrum and a nine-component NMR spectrum, it is demonstrated that the proposed algorithm is an effective adaptive immune algorithm. Compare with the IA-GA, the calculation speed of using the AIA is much faster and the resolved result is much more accurate.
With the aim of quantitative determination of multicomponent overlapping chromatograms, an improvement of the transmutation method was proposed with WT smoothing, cubic spline interpolation, and a new criterion for determination of the optimal points number. With the proposed algorithm, the oscillation generated in the transmutation process can be effectively suppressed. By the application to simulated
引文
[1] Ishida Y., An immune network model ad its applications to process diagnosis, Sys. Comp. Jpn., 1993, 24(6): 38-45
[2] Mori K., Tsukiyama M., Fukuda T., Application of an immune algorithm to multi-optimization problems, Electr. Eng. Jan., 1998, 122(2): 30-37
[3] Rob J. de B., Pauline H.,J. Theor. Biol., 1989, 139:17-38
[4] Chun J.S., Kyo H.K., Hahm S.Y., A study on comparison of optimization performances between immune algorithm and other heuristic algorithms, IEEE Transactions on Magnetics, 1998, 34(5): 2972-2975
[5] Vertosick F.T., Kelly R.H., Immune network theory: a role for parallel distributed processing, Immunology, 1989, 66:1-7
[6] Weinand R.G., Somatic mutation, affinity maturation and antibody repertoire: A computer model, Journal of Theoretical Biology, 1990, 143(3):343-383
[7] Maeder M., Evolving factor analysis for the resolution of overlapping chromatographic peaks, Anal. Chem., 1987, 59(3): 527-530
[8] Schostack K.J., Malinoski E.R., Investigation of window factor-analysis and matrix regression-analysis in chromatography, Chemometr. Intell. Lab. Syst., 1993, 20(2): 173-182
[9] Liang Y., Kvalheim O.M., Rahmani A., Brereton R.G., Resolution of strongly overlapping 2-way multicomponent data by means of heuristic evolving latent projections, J. Chemometr., 1993, 7:15-43
[10] Shao X.G., Cai W.S., Sun P.Y., Zhang M.S., Zhao G.W., Quantitative determination of the components in overlapping chromatographic peaks using wavelet transform, Anal. Chem., 1997, 69:1722-1725
[11] 邵学广，孙培艳，蔡文生，张懋森，小波变换及其在色谱重叠峰解析中的应用，化学通报，1997，(7)：54-57
[12] Shao X.G., Chen Z.H., Lin X.Q., An immune algorithm for resolution of multicomponent overlapping chromatograms, Fresenius' J. Anal. Chem, 1999, 366:10-16
[13] Shao X.G., Chen Z.H., Lin X.Q., Resolution of multicomponent overlapping chromatogram using an immune algorithm and genetic algorithm, Chemom. Intell. Lab. Sys., 2000, 50:91-99
[14] Shao X.G., Cai W.S., Sun P.Y., Determination of component number in the overlapping multicomponent chromatogram using wavelet transform, Chemometr. Intell. Lab., 1998, 43:147-155
[15] Shao X.G., Chen Z.H., Lin X.Q., An immune algorithm for resolution of multicomponent overlapping chromatograms, Fresenius' J. Anal. Chem, 2000, 366(1): 10-16
[16] 邵学广，孙莉，免疫算法用于多组分二维色谱数据的解析，分析化学，2001，29(7)：768-770
[17] Shao X.G., Cai W.S., Resolution of multicomponent chromatograms by window factor analysis with wavelet transform preprocessing, J. Chemometr., 1998, 12(2): 85-93
[18] Sun L., Cai W.S., Shao X.G., A two-dimensional immune algorithm for resolution of overlapping two-way chromatograms, Fresenius' J. Anal. Chem., 2001, 370(1): 16-21
[19] Mallat S.G., Multiresolution approximations and wavelet orthonormal bases of L2(R), Trans. Amer. Math. Soc., 1989, 315(1): 69-87
[20] Mallat S.G., A theory for multiresolution signal decomposition: the wavelet representation, IEEE trans. Pattern Anal. Machine Intell., 1989, 11:674-693
[21] Shao X.G., Yu Z.L., A fast algorithm based on wavelet compression and immune algorithm for resolution and quantitative determination of the component in multicomponent overlapping chromatogram, Chemical Journal on Internet, 2002, 4(8):048038pe
[22] 邵学广，王蕾，张孝松，免疫—遗传算法用于互变异构体重叠色谱峰的解析，化学通报(网络版)，Chemistry online，2003，66(5)：w037
[23] 邵利民，邵学广，林祥钦，一种基于免疫识别的主因子数判断方法，高等学校化学学报，2003，24(4)：595-598
[24] Malinowski E.R., Theory of error in factor analysis, Anal. Chem. 1977, 49(4): 606-612
[25] Malinowski E.R., Determination of the number of factors and the experimental error in a data matrix, Anal. Chem., 1977, 49(4): 612-617
[26] Wold S., Technometrics, 1978, 20(4): 397-405
[27] 邵学广，李梅青，邵利民，一种基于免疫算法的新型因子分析算法，高等学校化学学报，2002，23(7)：1269-272
[28] Su Q.D., Yang Y., Mao Q.L., Zhao G.W., Photoacoustic spectra of complexes of neodymium(Ⅲ) with glycine and alanine, Spectrosc. Lett., 1996, 29(4): 539-548
[29] Su Q.D., Wang Q., Lu J., Ni Q., Photoacoustic spectroscopy study on the luminescence properties of SM(3+) complexes, Spectrosc. Lett., 1996, 29(7): 1285-1295
[30] Zhang Y., Su Q.D., Zhao G.W., Spectra studies of complexes between palladium(Ii), nickel(Ii) and amino-acids, Spectrosc. Lett., 1992, 25(4): 521-533
[31] 邵学广，孙莉，免疫—遗传算法用于混合物重叠核磁共振信号解析，高等学校化学学报，2001，22(4)：552-555
[32] Shao X.G.,Yu Z.L., Sun L., Resolution of multicomponent NMR signals using wavelet compression and immune algorithm, Spectrochim. Acta A, 2003, 59(5):1075-1082
[33] Shao X.G., Wang G.Q., Wang S.F., Su Q.D., Extraction of mass spectra and chromatographic profiles from overlapping GC/MS signal with background, Anal. Chem., 2004, 76:5143-5148
[34] Shao X.G., Cheng L.G., Cai W.S., An adaptive immune optimization algorithm for energy minimization problems, J. Chem. Phys., 2004, 120(24): 11401-11406
[1] Mallat S.G., Multifrequency channel decompositions of images and wavelet models, IEEE T. Acoust. Speech, 1959, 37(12): 2091-2110
[2] Mallat S.G., Multiresolution Approximations and wavelet orthonormal bases of L2(R), Y. AM. MATH. SOC. 1989, 315(1): 69-87
[3] 秦前清，杨宗凯，实用小波分析，西安电子科技出版社，西安，1993
[4] 李世雄，小波变换及其应用，高等教育出版社，1997
[5] Young R.K., Rorword by Bose N.K., Kluwe Academic Publishers, Boston, Dordrecht, London, second printing, 1993
[6] Grossman A., Morlet J., SIAM Math. Anal., 1984, 15(4), 1723
[7] Cho K., Arias T.A., Joannopoulos J.D., Wavelets in electronic-structure calculations, Phys. Rev. Lett., 1993, 71(12): 1808-1811
[8] Askar A., Cetin A.E., Rabitz H., Wavelet transform for analysis of molecular dynamics, J. Phys. Chem., 1996, 100(49): 19165-19173
[9] Calais J.L., Wavelets - Something for quantum chemistry? Int. J. Quantum Chem., 1996, 58(6): 541-548
[10] Brewster M.E., Farm G.I., Yang Z.Y., Wavelets for electronic structure calculations, J Math. Chem., 1997, 22(2-4): 117-142
[11] Alsberg B.K., Woodward, A.M., Kell, D.B., An introduction to wavelet transforms for chemometricians: a time-frequency approach, Chemometr. Intell. Lab., 1997, 37(2): 215-239
[12] 郑建斌，赵瑞，张红权，张秀琦，赵小尊，仲红波，张懋森，小波变换及其在化学中的应用，分析化学 1999，27(07)：855-861
[13] Walczak B., Wavelet in chemistry, Elsevier Science Publishers B. V, Amsterdam, The Netherlands, 2000
[14] Ehrentreich F., Wavelet transform applications in analytical chemistry. Anal. Bioanal. Chem., 2001, 371(1): 115-121
[15] 邵学广，庞春艳，孙莉，小波变换与分析化学信号处理，化学进展，2000，12(3)：233-244
[16] Leung A.K., Chau F.T., Gao J.B., A review on applications of wavelet transform techniques in chemical analysis: 1989-1997, Chemometrics Intell. Lab. Syst., 1998, 43(1-2): 165-184
[17] Shao X.G., Leung A.K.M., Chau F.T., Wavelet: a new trend in chemistry, Acc. Chem. Res., 2003, 36(4): 276-283
[18] Chau F.T., Liang Y.Z., Gao J.B., Shao X.G., Chemometrics: from basics to wavelet transform, John Wiley & Sons, Hoboken, New Jersey, 2004
[19] Walczak B., Massart D.L., Wavelets - Something for analytical chemistry, Trends Anal. Chem., 1997, 16:451-463
[20] Shao X.G., Cai W.S., Wavelet analysis in analytical chemistry, Rev. Anal. Chem., 1998, 17:235-285
[21] Qin X., Shen L.S., Wavelet transform and its application in spectral analysis, Spectrosc. Spect. Anal., 2000, 20:892-897
[22] Jetter K., Depczynski U., Molt K., Niemoller A., Principles and applications of wavelet transformation to chemometrics, Anal. Chim. Acta, 2000, 420:169-180
[23] Chau F.T., Shih T.M., Gao J.B., Application of the fast wavelet transform method to compress ultraviolet-visible spectra, Appl. Spectrosc., 1996, 50(3): 339-348
[24] Chau F.T., Gao J.B., Shih T.M., Compression of infrared spectral data using the fast wavelet transform method, Appl. Spectrosc., 1997, 51 (5): 649-659
[25] Chau F.T., Tam K.Y., Application of the fast fourier-transform method for compression of spectral data obtained from a photodiode-array spectrophotometer, Comput. Chem., 1994, 18(1): 13-20
[26] Coifman R.R., Meyer Y., Quake S., Signal-processing and compression with wavelet packets, Progress in Wavelet Analysis and Applications, 1993, 77-93
[27] Mallat, S.G., A theory of multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern Anal. Machine Learning, 1989, 11:674-693
[28] Chau F.T., Shih T.M., Gao J.B., Application of the fast wavelet transform method to compress ultraviolet-visible spectra, Appl. Spectrosc., 1996, 50(3): 339-348
[29] Chau F.T., Gao J.B., Shih T.M., Compression of Infrared Spectral Data Using the Fast Wavelet Transform Method, Appl. Spectrosc., 1997, 51(5): 649-659
[30] Brown S.D., Sum S.T., Despagne F., Chemometrics, Anal. Chem., 1996, 68(12): R21-R61
[31] Brown S.D., Blank T.B., Sum S.T., Weyer L.G., Chemometrics, Anal. Chem., 1994, 66(12): R315-R359
[32] Walczak B., Massart D.L., Noise suppression and signal compression using the wavelet packet transform, Chemometr. Intell. Lab., 1997, 36(2): 81-94
[33] Barclay V.J., Bonner R.F., Hamilton I.P., Application of wavelet transforms to experimental spectra: smoothing, denoising, and data set compression, Anal. Chem., 1997, 69(1): 78-90
[34] Mittermayr C.R., Rosenberg E., Grasserbauer, M., Detection and estimation of heteroscedastic noise by means of the wavelet transform, Anal. Commun., 1997, 34(2): 73-75
[35] Shao X.G., Cai W.S., Sun P.Y., Zhang M.S., Zhao G.W., Quantitative determination of the components in overlapping chromatographic peaks using wavelet transform, Anal. Chem., 1997, 69:1722-1725
[36] 潘忠孝，邵学广，仲红波，刘卫，王洪，张懋森，小波变换用于高效液相色谱的基线校正，分析化学，1996，24(2)：149-153
[37] Tan H.W., Brown S.D., Wavelet analysis applied to removing non-constant, varying spectroscopic background in multivariate calibration. J. Chemometr., 2002, 16(5): 228-240
[38] Leung A.K., Chau F., Gao J.B., Wavelet transform: a method for derivative calculation in analytical chemistry, Anal. Chem., 1998, 70:5222-5229
[39] Nie L., Wu S.G., Lin X.Q., Zheng L.Z., Rui L., Approximate derivative calculated by using continuous wavelet transform, J. Chem. Info. Comp. Sci., 2002, 42:274-283
[40] 邵学广，侯树泉，方能虎，何友昭，赵贵文，小波变换用于植物激素重叠色谱峰中组分的定量分析，分析化学，1998，26(1)：107-110
[41] Shao X.G., Hou S.Q., On-line resolution of overlapping chromatograms using the wavelet transform, Anal. Sci. 1999, 15:681-684
[42] Shao X.G., Sun L., An application of the continuous wavelet transform to resolution of multicomponent overlapping analytical signals, Anal. Lett., 2001, 34(2): 267-280
[43] 邵学广，蔡文生，小波包分析用于重叠分析化学信号的处理，高等学校化学学报，1999，20(1)：42-46
[44] Shao X.G., Gu H,, Wu J.H., Shi Y.Y., Resolution of the NMR spectrum using wavelet transform, Applied Spectroscopy, 2000, 54(5): 731-738
[45] 刘辉，郑建斌，仲红波，小波模极大值滤噪法在示波计时电位信号处理中的应用，计算机与应用化学，2003，20(3)：269-273
[46] Shao X.G., Ma C.X., Application of adaptive wavelet algorithm to the resolution and quantitative analysis of overlapping multicomponent chromatogram, Anal. Lett., 2003, 36(6): 1261-1277
[47] 吴荣晖，邵学广，自适应小波算法用于近红外光谱的多元校正，分析化学，2005，33(7)：1010-1012
[48] Shao X.G., Ma C.X., A general approach to derivative calculation using wavelet transform, Chemometr. Intell. Lab., 2003, 69(1-2): 157-165
[49] Ma C.X., Shao X.G., Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra, J. Chem. Inf Comp. Sci., 2004, 44(3): 907-911
[50] 王国庆，王芳，陈达，苏庆德，邵学广，近红外光谱技术用于复杂植物样品中无机离子测定的新方法，光谱学与光谱分析，2004，24(12)：1540-1542
[51] 詹达琦，孙素琴，周群，秦竹，小波消噪与二维相关红外光谱的质量优化，光谱学与光谱分析，2004，24(12)：1549-1552
[52] 熊建辉，张普敦，郑育芳，许国旺，张玉奎，小波神经网络遗传算法用于2-(9-咔唑)乙基氯甲酸酯衍生化氨基酸的胶束电动力学色谱分离优化，分析科学学报，2004，20(3)：237-240
[53] 王瑛，莫金垣，化学信号的近似高阶导数计算，分析科学学报，2004，20(5)：453-457
[54] 王瑛，莫金垣，光谱信号的小波去噪新技术，光谱学与光谱分析，2005，25(1)：124-127
[55] 王立世，张永清，莫金垣，连续样条小波变换解析高噪声重叠分析信号，华南理工大学学报(自然科学版)，2005，33(2)：79-81
[56] 张水锋，王立世，张永清，费新平，党志，莫金垣，基于小波变换的循环伏安弱信号特征信息提取，分析化学，2005，33(4)：487-490
[57] 朱凤岗，朱雪田，连续小波变换用于滴定终点的确定，化学分析计量，2004，3：9-11
[58] 董林，许禄，二维小波变换与子窗口因子分析法结合用于含噪声HPLC-DAD数据的解析，高等学校化学学报，2005，26(6)：1039-1042
[59] 田高友，袁洪福，褚小立，刘慧颖，陆婉珍，结合小波变换与微分法改善近红外光谱分析精度，光谱学与光谱分析，2005，25(4)：516-520
[60] Esteban-Diez I., Gonzalez-Saiz J.M., Gomez-Camara D., Millan C.P., Multivariate calibration of near infrared spectra by orthogonal wavelet correction using a genetic algorithm, Anal. Chimica. ActA, 2006, 555 (1): 84-95
[61] Ramos P.M., Ruisanchez I., Data fusion and dual. domain classification analysis of pigments studied in works of art, Anal. Chim. Acta, 2006, 558(1-2): 274-282
[62] Daubechies I., Ten Lecture on Wavelet; SIAM press: Philadelphia, USA, 1992
[63] Chui C.K., Wang J.Z., A general framework of compactly support splines and wavelets, CAT report #219, Texas A&M University, 1990
[64] Chui C.K., Wang J.Z., An analysis of cardinal spline-wavelets, CA T report #231, Texas A&M University, 1990
[65] 胡昌华，张军波，夏军，张伟，基于MATLAB的系统分析与设计—小波分析，西安电子科技出版社，西安，2000
[1] Maeder M., Evolving factor analysis for the resolution of overlapping chromatographic peaks, Anal. Chem., 1987, 59(3): 527-530
[2] Schostack K.J., Malinowski E.R., Investigation of window factor-analysis and matrix regression-analysis in chromatography, Chemometr. Intell. Lab. Syst., 1993, 20(2): 173-182
[3] Shao X.G., Cai W.S., Sun P.Y., Zhang M.S., Zhao G.W., Quantitative determination of the components in overlapping chromatographic peaks using wavelet transform, Anal. Chem., 1997, 69: 1722-1725
[4] Shao X.G., Cai W.S., Sun P.Y., Determination of component number in the overlapping multicomponent chromatogram using wavelet transform, Chemometr. Intell. Lab. Syst., 1998, 43:147-155
[5] 邵学广，蔡文生，小波包分析用于重叠分析化学信号的处理，高等学校化学学报，1999，20(1)：42-46
[6] Shao X.G., Chen Z.H., Lin X.Q., Resolution of multicomponent overlapping chromatogram using an immune algorithm and genetic algorithm, Chemom. Intell. Lab. Sys., 2000, 50:91-99
[7] Shao X.G., Chen Z.H., Lin X.Q., An immune algorithm for resolution of multicomponent overlapping chromatograms, Fresenius J. Anal. Chem., 2000, 366(1): 10-16
[8] 邵学广，陈宗海，林祥钦，一种新型的信号拟合方法—免疫算法，分析化学，2000，28(2)：152-155
[9] Sun L., Cai W.S., Shao X.G., A two-dimensional immune algorithm for resolution of overlapping two-way chromatograms, Fresenius' J. Anal. Chem., 2001, 370(1): 16-21
[10] 邵学广，孙莉，免疫-遗传算法用于混合物重叠核磁共振信号解析，高等学校化学学报，2001，22(4)：552-555
[11] Pelezer J., Szalma S., Multidimensional NMR and data processing, Chem. Rev., 1991,91: 1507-1524
[12] Alsberg B.K., Kvalheim O.M., Compression of nth-order data arrays by b-splines .1. Theory, J. Chemometr., 1993, 7: 61-73
[13] Alsberg B.K., Kvalheim O.M., Speed improvement of multivariate algorithms by the method of postponed basis matrix multiplication . 1. Principal component analysis, Chemometr. Intell. Lab. Syst., 1994, 24: 31-42
[14] Alsberg B.K., Kvalheim O.M., Speed improvement of multivariate algorithms by the method of postponed basis matrix multiplication .2. 3-mode principal component analysis, Chemometr. Intell. Lab. Syst., 1994, 31: 43-54
[15] Walczak B., Massart D.L., Noise suppression and signal compression using the wavelet packet transform, Chemometr. Intell. Lab. 1997, 36(2): 81-94
[16] Chau F.T., Gao J.B., Shih T.M., Compression of infrared spectral data using the fast wavelet transform method, Appl. Spectrosc. 1997, 51(5): 649-659
[17] Mallat S.G., Multiresolution approximations and wavelet orthonormal bases of L2(R), T. AM. MATH. SOC, 1989, 315(1): 69-87
[18] Mallat S.G., A theory of multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern Anal. Machine Learning, 1989, 11: 674-693
[1] Maeder M., Evolving factor analysis for the resolution of overlapping chromatographic peaks, Anal. Chem., 1987, 59(3): 527-530
[2] Kvalheim O.M., Liang Y.Z., Heuristic evolving latent projections: resolving two-way multicomponent data. 1. selectivity, latent-projective graph, datascope, local rank, and unique resolution, Anal. Chem., 1992, 64(8): 936-946
[3] Malinowski E.R., Window factor-analysis--theoretical derivation and application to flow injection analysis data, J Chemom., 1992, 6(1): 29-40
[4] Gourvenec S., Lamotte C., Pestiaux P., Massart D.L., Use of the orthogonal projection approach (OPA) to monitor patch processes, Appl. Spectrosc., 2003, 57(1): 80-87
[5] Jiang J.H., Sasic, S., Yu R.Q., Ozaki Y., Resolution of two-way data from spectroscopic monitoring of reaction or process systems by parallel vector analysis (pva) and window factor, analysis (wfa): inspection of the effect of mass balance, methods and simulations, J Chemom., 2003, 17(3): 186-197
[6] Shao X.G., Leung A.K.M., Chau F.T., Wavelet: a new trend in chemistry, Accounts Chem. Res., 2003, 36(4): 276-283
[7] Shao L.M., Lin X.Q., Shao X.G., Wavelet transform and its applications in spectroscopic analysis, Appl. Spectrosc. Rev., 2002, 37(4): 429-450
[8] Kharintsev S.S., Sevastianov A.A., Salakhov M.K., Resolution enhancement of overlapping peaks in molecular spectra by derivative spectrometry method based on continuous wavelet transform, Asian J. Spectrosc., 2002, 6(4): 145-154
[9] Zhang X.Q., Jin J.Y., Zheng J.B., Gao H., Genetic algorithms based on wavelet transform for resolving simulated overlapped spectra, Anal. Bioanal. Chem., 2003, 377(7-8): 1153-1158
[10]Dinc E., Baleanu D., Ustundag O., An approach to quantitative two-component analysis of a mixture containing hydrochlorothiazide and spironolactone in tablets by one-dimensional continuous daubechies and biorthogonal wavelet analysis of UV-spectra, Spectrosc. Lett., 2003, 36(4): 341-355
[11]Shao X.G., Yu Z.L., Sun L., Immune algorithms in analytical chemistry, TRAC-Trend. Anal. Chem., 2003, 22(2): 59-69
[12]Shao X.G., Chen Z.H., Lin X.Q., An immune algorithm for resolution of multicomponent overlapping chromatograms, Fresenius J. Anal. Chem., 2000, 366(1): 10-16
[13] Shao X.G., Chen Z.H., Lin X.Q., Resolution of multicomponent overlapping chromatogram using an immune algorithm and genetic algorithm, Chemom. Intell. Lab. Syst.,2000,50(1):91-99
[14] Shao X.G., Sun L., Resolution of multicomponent overlapping nmr signals using an immune algorithm and genetic algorithm, Anal Lett., 2002, 35(14): 2375-2387
[15] Shao X.G., Yu Z.L., Sun L., Resolution of multicomponent nmr signals using wavelet compression and immune algorithm, Spectrochim. Acta. A., 2003, 59(5): 1075-1082
[1] Chen J.C., Rutan S.C., Identification and quantification of overlapped peaks in liquid chromatography with UV diode array detection using an adaptive Kalman filter, Anal. Chim. Acta, 1996, 335(1-2): 1-10
[2] Maeder M., Evolving factor analysis for the resolution of overlapping chromatographic peaks, Anal. Chem., 1987, 59(3): 527-530
[3] Schostack K.J., Malinoski E.R., Investigation of window factor-analysis and matrix regression-analysis in chromatography, Chemometr. Intell. Lab. Syst., 1993,20(2): 173-182
[4] Malinowski E.R., Window factor-analysis — Theoretical derivation and application to flow injection analysis data, J. Chemom., 1992, 6: 29-40
[5] Kvalheim O.M., Liang Y.Z., Heuristic evolving latent projections: resolving two-way multicomponent data 1: selectivity, latent-projective graph, datascope, local rank, and unique resolution, Anal. Chem., 1992, 64: 936-946
[6] Shao X.G., Cai W.S., Sun P.Y., Zhang M.S., Zhao G.W., Quantitative Determination of the Components in Overlapping Chromatographic Peaks Using Wavelet Transform, Anal. Chem. 1997,69: 1722-1725
[7] Shao X.G., Leung A.K.M., Chau F.T., Wavelet: a new trend in chemistry. Acc. Chem. Res., 2003, 36(4): 276-283
[8] Shao X.G., Cai W.S., Pan Z.X., Wavelet transform and its applications in high performance liquid chromatography(HPLC) analysis, Chemom. Intell Lab. Syst., 1999, 45(1-2): 249-256
[9] Shao X.G., Chen Z.H., Lin X.Q., Resolution of multicomponent overlapping chromatogram using an immune algorithm and genetic algorithm, Chemom. Intell. Lab. Syst, 2000, 50(1): 91-99
[10]Shao X.G., Yu Z.L., Sun L., Immune algorithms in analytical chemistry, TRAC-Trend. Anal. Chem., 2003, 22(2): 59-69
[11]Malinowski E.R., Resolving and quantifying overlapped chromatographic bands by transmutation, Anal. Chem., 2000, 72(18): 4363-4371
[12]Malinowski E.R., A Theoretical study of the transmutation method for resolving and quantifying overlapped chromatographic bands. J. Chemom., 2002, 16: 54-67
[13]Foley J.P., Equations for chromatographic peak modeling and calculation of peak area, Anal. Chem., 1987, 59: 1984-1987
[14]Jetter K., Depczynski U., Molt K., Niemoller A., Principles and applications of wavelet transformation of chemometrics, Anal. Chim. Acta., 2000, 420: 169-180
[15]Walczak B., Massart D.L., Wavelets - Something for analytical chemistry? TrAC-Trends Anal. Chem., 1997, 16: 451-463
[16]Mallat S.G., Multiresolution approximations and wavelet orthonormal bases of L~2(R), Trans. Amer. Math. Soc, 1989, 315: 69-87
[17]Mallat S.G., A theory for multiresolution signal decomposition: the wavelet representation, IEEE trans. Pattern Anal. Machine Intell., 1989, 11: 674-693
[1] Shao X.G., Sun L., Resolution of multicomponent overlapping NMR signals using an immune algorithm and genetic algorithm, Anal. Lett., 2002, 35(14): 2375-2387
[2] Shao X.G., Yu Z.L., Sun L., Resolution of multicomponent NMR signals using wavelet compression and immune algorithm, Spectrochimica Acta Part A, 2003, 59(5): 1075-1082
[3] Shao X.G., Gu H., Wu J.H., Shi Y.Y., Resolution of the NMR Spectrum Using Wavelet Transform, Applied Spectroscopy, 2000, 54(5): 731-738
[4] Hyvarinen A., Karhunen J., Oja E., Independent Component Analysis, John Wiley & Sons, 2001
[5] Hyvarinen A., Oja E., Independent component analysis: algorithms and applications, Neural Networks, 2000, 13(4-5): 411-430
[6] Lathauwer L.De, Moor B.De, Vanderwalle J., An introduction to independent component analysis, J Chemometr., 2000, 14:123-149
[7] Stone J.V., Independent component analysis: an introduction, Trends Cogn. Sci., 2002, 6(2): 59-64
[8] Makeig S., Westerfield M., Jung T.P., Enghoff S., Townsend J., Courchesne E., Sejnowski T.J., Dynamic brain sources of visual evoked responses, Science, 2002, 295(5555): 690-694
[9] Back A.D., Weigend A.S., A first application of independent component analysis to extracting structure from stock returns, International J. of Neural Sys., 1997, 8(4): 473-484
[10] Visser E., Lee T.W., An information-theoretic methodology for the resolution of pure component spectra without prior information using spectroscopic measurements, Chemometr. Intell. Lab., 2004, 70:147-155
[11] 毕贤，李通化，吴亮，独立组分分析在红外光谱分析中的应用，高等学校化学学报，2004，25(6)：1023-1027
[12] Chen J., Wang X.Z., A new approach to near-infrared spectral data analysis using independent component analysis, J. Chem. Inf Comp. Sci., 2001, 41: 992-1001
[13] Pichler A., Sowa M.G., Independent component analysis of photoacoustic depth profiles, J. Mol. Spectrosc., 2005, 229(2): 231-237
[14] Shao X.G., Wang G.Q., Wang S.F., Su Q.D., Extraction of mass spectra and chromatographic profiles from overlapping GC/MS signal with background, Anal. Chem., 2004, 76:5143-5148
[15] Ren J.Y., Chang C.Q., Fung P.C.W., Shen J.G., Chan F.H.Y., Free radical EPR spectroscopy analysis using blind source separation, J. Magnetic Reson., 2004, 166(1): 82-91
[16] Bell A.J., Sejnowski T.J., An information maximization approach to blind separation and blind deconvolution, Neural Computation, 1995, 7(6): 1129-1159
[17] Cardoso J.F., Souloumiac A., Blind beam forming for non-Gaussian signals, Proc. Inst. Electr. Eng. F, 1993, 40(6): 362-370
[18] Hyvarinen A., Oja E., A fast fixed point algorithm for independent component analysis, Neural Computation, 1997, 9:1483-1492
[19] Hyvairinen A., Fast and robust fixed-point algorithms for independent component analysis, IEEE Trans. neural networks, 1999, 10:626-634
[20] 邵学广，孙莉，免疫-遗传算法用于混合物重叠核磁共振信号解析，高等学校化学学报，2001，22(4)：552-555