参考文献

参考文献

[1] HAAR A. Zur Theorie der orthogonalen Funktionensysteme[J]. Math Annalen,1910(69):331-371.

[2] GABOR D. Theory of communication[J]. J Inst Elect Eng,1946(93):429-457.

[3] GROSSMANN A, MORLET J. Decomposition of hardy functions into square integrable wavelets of constant shape[J]. SIAM J Math Anal,1984(15):723-736.

[4] MEYER Y. Principe d’incertitude, bases hilbertiennes et algebres d’operateurs[J].Bourbaki Seminar,1985(38):209-223.

[5] MALLAT S G. Multiresolution approximations and wavelet orthonormal bases of L2(R) [J]. Trans Amer Math Soc,1989,315(1):69-87.

[6] MEYER Y. Ondelettes et operateurs I: Ondelettes[J]. Hermann, 1991(3):253-264.

[7] DAUBECHIES I. Orthonormal bases of compactly supported wavelets[J]. Commun on Pure Appl Math,1988,41(7):909-996.

[8] COHEN A, DAUBECHIES I, FEAUVEAU J C. Biorthogonal bases of compactly supported wavelets[J]. Commun on Pure Appl Math,1992(45):485-560.

[9] DAUBECHIES I. Ten lectures on wavelets,CBMS-NSF regional conference series in applied mathematics[M]. Philadelphia: SIAM,1992.

[10] 程正兴.小波分析算法与应用[M].西安:西安交通大学出版社,1998.

[11] 程正兴,杨守志,冯晓霞.小波分析的理论　算法　进展和应用[M].北京:国防工业出版社,2007.

[12] 崔锦泰.小波分析导论[M].程正兴,译.西安:西安交通大学出版社,1995.

[13] 梁学章,何甲兴,王新民,等,小波分析[M].北京:国防工业出版社,2005.

[14] BENEDETTO J J, FRAZIER M W. Wavelets: mathematics and applications[M].Florida: CRC Press,1994.

[15] COHEN A. Numerical analysis of wavelet methods[M]. Amsterdam: North-Holland,2003.

[16] LOUIS A K, MAAB P, RIEDER A. Wavelets: theory and applications[M]. Chichester: John Wiley Sons, Incs.,1997.

[17] MALLAT S. A wavelet tour of signal processing[M]. 2nd ed. San Diego: Academic Press,1999.

[18] WOJTASZCZYK P. A mathematical introduction to wavelets[M]. Cambridge:Cambridge University Press,1997.

[19] HEIL C, WALNUT D F. Fundamental papers in wavelet theory[M]. Princeton:Princeton University Press,2006.

[20] XIA X G, ZHANG Z. On sampling theorem, wavelets and wavelet transforms[J].IEEE Trans Signal Process,1993,41(12):3524-3525.

[21] ALPERT B K. A class of bases in L2 for the sparse representations of integral operators[J]. SIAM J Math Anal,1993,24(1):246-262.

[22] BOOR C D, DEVORE R, RON A. On the construction of multivariate (pre)wavelets[J]. Constr Approx,1993(9):123-166.

[23] GOODMAN T N T, LEE S L, TANG W S. Wavelets in wandering subspaces[J].Trans Amer Math Soc,1993,338(2):639-654.

[24] HERVE L. Multi-resolution analysis of multiplicity d: applications to dyadic interpolation[J]. Appl Comput Harmon Anal,1994(14):299-315.

[25] GERONIMO J S, HARDIN D P, MASSOPUST P R. Fractal functions and wavelet expansions based on several scaling functions[J]. SIAM J Math Anal, 1994, 78(3):373-401.

[26] DAHLKE S, GRÖCHENIG K, MAASS P. A new approach to interpolating scaling functions[J]. Appl Anal,1999,72(3/4):485-500.

[27] DAHLKE S,MAAβ P. Interpolating refinable and wavelets for general scaling[J].Numer Funct Anal Optim,1997,18(5/6):521-539.

[28] COHEN A, DAUBECHIES I, PLONKA G. Regularity of refinable function vectors[J].J Fourier Anal Appl,1997(3):295-324.

[29] MICCHELLI C A, SAUER T. Continuous refinable functions and self similarity[J]. Vietnam Math,2003,31(4):449-464.

[30] SHEN Z W. Refinable function vectors[J]. SIAM J Math Anal, 1998, 29(1):235-250.

[31] STRELA V, WALDEN A T. Signal and image denoising via wavelet thresholding:orthogonal and biorthogonal, scalar and multiple wavelet transforms[M]. Cambridge: Cambridge University Press,2000.

[32] SELESNICK I W. Interpolating multiwavelet bases and the sampling theorem[J].IEEE Trans Signal Process,1999,47(6):1615-1621.

[33] HAN B. Symmetric multivariate orthogonal refinable functions[J]. Appl Comput Harmon Anal,2004,17(3):277-292.

[34] DERADO J. Nonseparable, compactly supported interpolating refinable function with arbitrary smoothness[J]. Appl Comput Harmon Anal, 2001, 10 (2):113-138.

[35] DESLAURIERS G, DUBOIS J, DUBUC S. Multidimensional iterative interpolation[J]. Can J Math,1991(43):297-312.

[36] HAN B, JIA R Q. Optimal interpolatory subdivision schemes in multidimensional spaces[J]. SIAM J Math Anal,1998,36(1):105-124.

[37] HAN B, JIA R Q. Quincunx fundamental refinable functions and quincunx biorthogonal wavelets[J]. Math Comput,2002(71):165-196.

[38] RIEMENSCHNEIDER S D, SHEN Z W. Multidimensional interpolatory subdivision schemes[J]. SIAM J NVumer Anal,1997,34(6):2357-2381.

[39] RIEMENSCHMEIDER S D, Shen Z W. Construction of compactly supported biorthogonal wavelets in L2(Rd) II, Wavelet Applications in Signal and Image Processing VII[C]/ /Proceedings of the SPIEE 1999:264-272.

[40] CHUI C K, JIANG Q T. Matrix-valued symmetric templates for interpolatory surface subdivisions: I. Regular vertices[J]. Appl Comput Harmon Anal, 2005, 19(3):303-339.

[41] CONTI C, ZIMMERMANN G. Interpolatory rank-1 vector subdivision schemes[J]. Comput Aided Geom Des,2004,21(4):341-351.

[42] HAN B, YU T P Y, PIPER B. Multivariate refinable hermite interpolant[J].Math Comput,2004,73(248) :1913-1935.

[43] HAN B. Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix[J]. J Comput Appl Math,2003(155):43-67.

[44] HAN B. Vector cascade algorithms and refinable function vectors in Sobolev spaces[J]. J Approx Theory,2003,124(1):44-88.

[45] HAN B. Approximation properties and construction of Hermite interpolants and biorthogonal multiwavelets[J]. J Approx Theory,2001,110(1):18-53.

[46] JIA R Q, MICCHELLI C A. On linear independence of integer translates of a finite number of functions[J]. Proc. Edinburg Math Soc,1992,36(1):69-85.

[47] JIA R Q, JIANG Q T. Spectral analysis of the transition operator and its applications to smoothness analysis of wavelets[J]. SIAM Matric Anal Appl, 2003, 24:1071-1109.

[48] HAN B. Solution in Sobolev spaces of vector refinement equations with a general dilation matrix[J]. Adv Comput Math,2006(24):375-403.

[49] KOCH K. Interpolating scaling vectors[J]. Int J Wavelets Multiresolution Info Process,2005,3(3):389-416.

[50] KOCH K. Multivariate orthonormal interpolating scaling vectors[J]. Appl Comput Harmon Anal,2007,22(2):198-216.

[51] HAN B, KWON S G, ZHUANG X S. Generalized interpolating refinable function vectors[J]. J Comput Appl Math,2009,227(2):254-260.

[52] 孙佳宁.多元插值型可加细函数的构造与小波在图像隐藏技术中的应用[D].长春:吉林大学,2008.

[53] EHLER M. On multivariate compactly supported bi-frames[J]. J Fourier Anal Appl,2007,13(5):511-532.

[54] ZHOU D X. Interpolatory orthogonal multiwavelets and refinable functions[J].IEEE Trans Signal Process,2002,50(3):520-527.

[55] HAN B. The initial functions in a cascade algorithm[C]/ /Proceedings of Inter-national Conference of Computational Harmonic Analysis,2002.

[56]CHUI C K, LI C. A general framework of multivariate wavelets with duals[J]. Appl Comput Harmon Anal,1994,1(4):368-390.

[57] LEBRUN J, VETTERLI M. Balanced multiwavelets: theory and design[J]. IEEE Trans Signal Process,1998,46(4):1119-1125.(https://www.daowen.com)

[58] CHUI C K, JIANG Q T. Multivariate balanced vector-valued refinable functions,Modern developments in multivariate approrimation[C]/ /Proceedings of the 5th international conference,2003,145:71-102.

[59] HAN B. Bivariate (Two-dimensional) Wavelets[M]. New York: Springer,2009.

[60] HAN B. Symmetry property and construction of wavelets with a general dilation matrix[J]. Linear Algebra Appl,2002,353(1-3):207-252.

[61] CABRELLI C, HEIL C, MOLTER U. Accuracy of lattice translates of several multidimensional refinable functions[J]. J Appror Theory,1998(95):5-52.

[62] CHEN D R, HAN B, RIEMENSCHNEIDER S D. Construction of multivariate biorthogonal wavelets with arbitrary vanishing moments[J]. Adv Comput Math,2000,13(2):131-165.

[63] CHUI C K, HE W J, STÖCKLER J. Compactly supported tight and sibling frames with maximum vanishing moments[J]. Appl Comput Harmon Anal, 2002, 13(3):224-262.

[64] CHUI C K, JIANG Q T. Balanced multi-wavelets in Rs[J]. Math Comput,2005,74(251):1323-1344.

[65] CHUI C K, MHASKAR H N. On trigonometric wavelets[J]. Constr Approx,1993,9(2):167-190.

[66] NARCOWICH F J, WARD J D. Wavelets associated with periodic basis functions[J]. Appl Comput Harmonic Anal,1996,3(1):40-56.

[67] PLONKA G, TASCHE M. Periodic splines and wavelets[R]. Mathematik: Universitat Rostock,1993.

[68] PLONKA G, TASCHE M. On the computation of periodic spline wavelets[J]. Applied and Computational Harmonic Analysis,1995(2):1-14.

[69] PLONKA G, TASCHE M. A unified approach to periodic wavelets[J]. Wavelet Analysis and Its Applicatioins,1994(5):137-151.

[70] KOH Y W, LEE S L, TAN H H. Periodic orthogonal splines and wavelets[J].Applied and Computational Harmonic Analysis,1995,2(3):201-218.

[71] CHEN H L. Construction of orthonormal wavelets in the periodic case[J]. Chinese Science Bulletin,1996(14):552-554.

[72] CHEN H L, XIAO S L. Periodic cardinal interpolatory wavelets[J]. Chin Ann of Math,1998(2):133-142.

[73] CHEN H L, LI D F. Construction of multidimensional biorthogonal periodic multiwavelets [J]. Chinese Journal of Contemporary Mathematics, 2000 (21):223-232.

[74] CHEN H L, LIANG X Z, PENG S L, et al. Real-valued periodic wavelets: construction and relation with Fourier series[J]. J Comp Math, 1999, 17(5):509-522.

[75] 李登峰,彭思龙,陈翰麟. 一类周期小波的局部性质[J]. 数学学报, 2001, 44(5):947-960.

[76] CHEN H L, PENG S L. Local properties of cardinal interpolatory function[J].ACTA Math Sinica (English Series),2001,17(4):613-620.

[77] 彭思龙, 李登峰, 湛秋辉. 周期小波理论及其应用[M]. 北京:科学出版社,2003.

[78] GOH S S, LEE S L, TEO K M. Multidimensional periodic multiwavelets[J]. J Approx Theory,1999,98(1):72-103.

[79] SCHOENBERG I J. Contributions to the problem of approximation of equidistant data by analytic functions[J]. Appl Math,1946(4):45-99.

[80] BOOR C D,DEVORE R. Approximation by smooth multivariate splines[J]. Trans Amer Math Soc,1983,276(2):775-788.

[81] CHUI C K. Multivariate Splines[M]. Philadelphia : SIAM Publication,1988.

[82] DAHLEN M. On the evaluation of box splines[M]. New York: Academic Press,1989.

[83] BOOR C D. On the evaluation of box splines[J]. Numer Algorithms, 1993(5):5-23.

[84] BOOR C R D, HÖLLIG K, RIEMENSCHNEIDER S D. Box Splines[M]. New York: Springer-Verlag,1993.

[85] KOBBELT L. Stable evaluation of box-splines[J]. Numer Algorithms,1997(14):377-382.

[86] 梁学章,金光日.二元样条与小波[C]/ /天津数学计算年会文集,2003.

[87] CHUI C K, STCKLER J, WARD J D. Compactly supported box-spline wavelets[J]. Approx Theory Appl,1992(3):77-100.

[88] RIEMENSCHNEIDER S D, SHEN Z W. Wavelets and pre-wavelets in low dimensions[J]. J Approx Theory,1992,71(1):18-38.

[89] HE W J, LAI M J. Construction of bivariate compactly supported biorthogonal box spline wavelets with arbitrarily high regularities[J]. Appl Comp Harm Anal,1999(6):53-74.

[90] LIANG X Z, JIN G R, CHEN H L. Bivariate box-spline wavelets[M]. Kluwer:Academic Publishers,1995.

[91] SUN J C. Multivariate Fourier series over a class of non tensor-product partition domains[J]. J Comp Math,2003(1):53-62.

[92] 李强,梁学章. 平行六边形上的周期正交小波[J]. 吉林大学学报(理学版),2005,43(2):142-148.

[93] LI Q,SU L T,LIANG X Z. Implementation of fast algorithms for biorthogonal periodic interpolatory wavelets[J]. Journal of Information and Computational Science,2007,4(2):545-552.

[94] SHIMIZU K. Optical trans-body imaging-feasibility of optical CT and functional imaging of living body[J]. Medicina Philosophica,1992(11):620-629.

[95] KONO M, UEKI H, UMEMURA S I. Near-infrared finger vein patterns for personal identification[J]. Applied Optics,2002,41(35):7429-7436.

[96] MIURA N, NAGASAKA A, MIYATAKE T. Feature extraction of finger vein patterns based on iterative line tracking and its application to personal identification[J]. Systems and Computers in Japan,2004,35(7):61-71.

[97] WEN X B, LIANG X Z, ZHANG J L. A new algorithm for enhancing the contrast of finger-vein image[J]. Journal of Information and Computational Science,2006(3):929-934.

[98] 温学兵,赵江魏,梁学章.基于小波去噪和直方图模板均衡化的手指静脉图像增强[J].吉林大学学报(理学版),2008,46(2):291-293.

[99] 李铁钢. 静脉识别算法研究[D].长春: 吉林大学,2007.

[100] IM S K, CHOI H S, KIM S W. A Direction-based vascular pattern extraction algorithm for hand vascular pattern verification[J]. ETRI Journal, 2003, 25(2):101-108.

[101] IM S K, PARK H M, KIM Y W, et al. An biometric identification system by extracting hand vein patterns[J]. Journal of the Korean Physical Society,2001,38(3):268-272.

[102] TANAKA T, KUBO N. Biometric authentication by hand vein patterns[C]/ /SICE 2004 Annual Conference,2004.

[103] CROSS J M, SMITH C L. Thermographic imaging of the subcutaneous vascular network of the back of the hand for biometric identification[C]/ /Proceedings Institute of Electrical and Electronics Engineers 29th Annual 2005 International Carnahan Conference on Security Technology,2005.

[104] BADAWI A M. Hand vein biometric verification prototype: a testing performance and patterns similarity[C]/ /Proceedings of The 2006 International Conference on Image Processing,Computer Vision, and Pattern Recogni-tion,2006.

[105] WANG L Y, LEEDHAM G. A thermal hand vein pattern verification system[J].Pattern Recognition and Image Analysis,2005(3687):58-65.

[106] ZHANG Y, HAN X, MA S L. Feature extraction of hand-vein patterns based on ridgelet transform and local interconnection structure neural network[J]. Lecture Notes in Control and Information Sciences,1970(345):870-875.

[107] 周斌,林喜荣,贾惠波,等. 多特征融合的手背血管识别算法[J].清华大学学报(自然科学版),2007,47(2):194-197.

[108] 张晋阳,孙懋珩.手背静脉图像骨架特征提取的算法[J].计算机应用,2007,27(1):152-154.

[109] 吕佩卓,赖声礼,陈佳阳,等.一种自适应的手背静脉区域定位算法[J].微计算机信息,2008,24(4):208-209,296.

[110] 林喜荣,庄波,苏晓生,等.人体手背血管图像的特征提取及匹配[J].清华大学学报(自然科学版),2003,43(2):164-167.

[111] 王科俊,丁宇航,王大振. 基于静脉识别的身份认证方法研究[J].科技导报,2005,23(1):35-37.

[112] 张会林,简献忠.人体手背静脉血管图像增强处理算法研究[J].仪器仪表学报,2005,26(增刊8):729-731.

[113] SHENSHA M J. The discrete wavelet transform: wedding the a trous and mallat algorithms[J]. IEEE Trans Signal Processing,1992,40(10):2464-2482.

[114] DONOHO D L, JOHNSTONE I M. Ideal spatial adaptation by wavelet shrinkage[J]. Biometrika,1994,81(3):425-455.