超声多普勒内窥成像系统及信号处理的研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
近十几年来,随着各种电子系统的应用和换能器技术的发展,超声医学诊断仪器被广泛应用于临床医学。其中多普勒血流检测超声内窥镜系统具有深度定位能力,能较好的对血流速度进行定量检测,可以更加准确地判断病变情况,得到了广泛的应用。
     本论文针对超声多普勒内窥成像提出全数字化的信号处理方案,实现了对内窥镜下小探头获得的多普勒微弱信号的处理,利用现场可编程门阵列(Field Programmable Gate Array, FPGA)实现信号的解调和频谱分析,并进行基于多普勒物理模型的成像实验,对超声内窥成像系统的正确性进行验证。主要内容包括:
     1.介绍脉冲多普勒检测技术的原理、信号模型,并针对血流自身的动力学特征及其对信号在频域上分布的影响,确定并完成超声脉冲多普勒系统的整体方案:设计脉冲多普勒系统的距离选通装置,提取目标不同深度处的血流速度信息;完成多普勒信号正交解调环节,使信号降至基频;设计FIR高通滤波器,避免血管及低速血流对信号的干扰;利用短时傅立叶变换完成频谱分析,并用动态功率谱图的形式,形象地反映血流的方向、速度等信息。
     2.目前有关基于内窥镜小探头的微弱超声多普勒信号检测的研究很少,本文针对超声内窥成像系统提出全数字化的多普勒回波信号处理方案。针对内窥系统超声探头体积小,回波信号微弱的特点,设计具有较高增益和较低噪声的超声信号前端接收电路。在FPGA中对微弱信号进行全数字化处理,实现正交解调与频谱分析等功能,系统具有电路匹配性好、信噪比高、处理速度快,体积小等优势。
     3.针对频谱多普勒系统自身的噪声和外来干扰对谱图的影响,综合小波分析在多普勒超声信号降噪和血管壁信号消除中的应用,提出一种新的超声多普勒信号分析系统设计框架。首先介绍小波变换,然后针对小波变换的缺点,给出信号的自适应描述,包括小波包和小波框架,最后介绍基于这些变换和取阈值的降噪方法及其时移不变性的获得方法,并利用基于小波框架及其时移不变特性的降噪方法对多普勒超声信号进行降噪。为了避免直接降噪复信号时,阈值非线性引起的相位扭曲,结合非固定取阈值方法,设计出一种多普勒超声信号降噪模式,并结合Matlab给出具体的实验方法和实验结果。
     4.搭建基于多普勒物理模型的成像实验平台,验证系统正确性。首先介绍多普勒物理模型实验平台的组成及实验方法。设计三组实验——静态血流模型、双路同向血流模型和双路异向血流模型,分析血流的速度与方向改变时,系统所得动态功率谱图的情况,证明硬件电路可以判断血流速度的快慢、辨别血流方向以及具有距离选通的功能,以此证明系统方案的可行性及正确性。
     本论文具有以下几个创新点:
     1、针对内窥镜小探头的微弱超声多普勒信号检测,设计并实现了具有较高增益和较低噪声的超声信号接收系统,在FPGA中对微弱信号进行全数字化处理,实现了正交解调与频谱分析等功能,系统具有电路匹配性好、信噪比高、处理速度快、体积小等优势。
     2、考虑到血流多普勒回波信号的时频特性及所携杂波的时变性、复杂性,本文应用基于小波冗余框架理论的非正交小波降噪方法,同时结合“区间能量最小”优化准则,设计了一种新型血流多普勒超声信号优化模型,通过增加适量的冗余性,来克服正交、双正交小波在信号去噪方面的不足,同时又极大地改善了小波框架的逼近空间与信号空间不匹配产生的边界畸变失真。通过数值仿真,本文设计的这种滤噪方案在信噪比改善(dB)、平均频率波形均方根误差(Hz)、谱宽波形均方根误差(Hz)等指标方面,具有比其它滤波方式更好的效果。通过实验模拟平台所得的数据处理结果验证了这一结论。
     3、根据血流多普勒超声信号在各尺度小波分析上的特点,针对硬阈值和软阈值算法的缺陷,采用一种新的Semisoft阈值函数,并结合二次B样条小波,通过仿真将它与软阈值、硬阈值及非负Garrote阈值进行数值对比分析,结果表明,基于Semisoft阈值法的二次B样条小波框架方法获得了最优的性能改善。
During the past decades, ultrasonic medical diagnostic instruments have advanced significantly as a result of the resourceful application of electronic-system and transducer designs to the problem of noninvasive information acquisition from clinical patients. Medical Doppler ultrasonic endoscope system bases on ultrasonic endoscope system, combining the advantage of ultrasound in diagnosis with the sensitivity of Doppler to moving objects together. The Pulsed Doppler Quantitative detection can be measured by Doppler blood velocity profile. In this way, we get histology characteristic of digestive organ wall’s sections and the hemodynamics parameters on sections. The information helps us make judgments about pathological changes in upper gastrointestinal tract.
     This paper depicts the development of a Doppler ultrasonic endoscope imaging system based on FPGA. In order to capture the weak signal scattered from tissue, the ultrasound signal reception circuit with high gain and low noise level was designed. All-digital signal processing was utilized to process the weak signal in FPGA, and the quadrate demodulation and spectrum analysis were realized. The experiment platform based on the Doppler physical model was set up to verify the performance of the system. By comparing the sonogram under different situations, the system and signal processing method are proved reasonable and correct.
     This paper consists of 4 parts as follows:
     1. Introduce the theory and signal modal of ultrasonic pulse Doppler technique, design the integral system scheme based on hemodynamic features and its spectral influence. A distance switch was used in this system to extract information of blood flow rate. Furthermore, a quadrature demodulation module and a FIR high pass filter were adopted to depress noise from vessel and low velocity blood. Then dynamic spectral map was introduced to depict direction and velocity information of blood simultaneously.
     2. Currently, study of weak signal collected from small endoscope probe is still not popular. To overcome the low volume and weak amplitude problem in ultrasonic endoscope, this paper designs a totally digital process scheme for ultrasonic echo signals, and a receipt circuit with high gain and low noise. Quadrature demodulation and spectral analysis were operated in FPGA. The circuit shows advantages of well matching, high SNR, low volume and rapid process.
     3. A novel analysis frame on ultrasonic signal, which integrate wavelet analysis advantage on signal denoise and vessel noise removing, was developed to depress the influence of system noise and input artifacts. In this part we introduce wavelet transform firstly and then present the signal self adaptive description, which contains wavelet pack and wavelet frame. Finally we introduce the threshold denoising method based on wavelet frame transformation and time-invariant performance. To overcome the phase confusion in directly complex signal transformation, a denoise module integrated with non-fixed threshold method was designed and experiment results on Matlab was also presented.
     4. Construct the image experiment platform of Doppler modal and evaluate the correctness of system. In this part, constitutes and experiment method were introduced firstly. Three group experiments: static blood flow modal, dual path same direction blood flow modal, dual path different direction blood flow modal was operated in this part and the blood flow characters in these experiments were analyzed. Results of spectral map in blood velocity and direction changing shows that the circuit in this part has the ability to judge blood velocity and direction, specifically, it also has the distance switch function. Consenquently this scheme is reasonable and correct.
     Innovations of this paper are :
     1. For weak signal detection under ultrasonic endoscope micro probe, a receipt circuit with high gain and low noise was designed and realized. Quadrature demodulation and spectral analysis were operated in FPGA. The circuit of this system shows advantages of well matching, high SNR, low volume and rapid process.
     2. Under the consideration of the time-variance and complexity in mixed ultrasonic echo wave signals a novel signal optimization modal was designed, which combined nonorthogonal wavelet based on wavelet frame redundancy theory with interval power minimum optimization rules. Through improve the redundancy properly, this method overcome the limitation of orthogonal and biorthogonal wavelet on the denoising and reform the boundary distortion from the mismatch between wavelet frame approximate space and signal space. Results of value simulation expressed higher SNR, lower root mean square error of mean frequency waveform and spectral range waveform. Moreover, the experiment results also demonstrated this conclusion.
     3. Based on the multi scale wavelet character of blood ultrasonic Doppler signals, a novel semisoft threshold function was adopted in this paper to overcome the flaw of hard threshold and soft threshold algorithms. The comparison analysis with soft threshold, hard threshold and non-negetive Garrote threshold were operated combined with Quadratic B-Spline wavelet, the results showed that BWTF method based on semisoft threshold achieved the best performance.
引文
[1]王威琪,徐智章,汪源源等.医学超声工程现状和生物医学超声概况.声学技术,1994, 13(1): 27~35
    [2]冯若,刘忠齐,姚锦钟等,超声诊断设备原理与设计,北京:中国医药科技出版社,1993
    [3]张凯,周铁英,三种弯曲旋转超声电机的原理及研究,压电与声光,2002,24(3): 191~195
    [4] Kasai C., Namekawa K., Koyano A., et al., Real-time two-dimensional blood flow imaging using an autocorrelation technique, IEEE Trans. Son. Ultrason.,1985, SU-32: 458~464
    [5] Wang Zhiqiang, Wang Jiandong, Wang Xiangdong, Colour Doppler endoscopic ultrasonography in differential diagnosis of benign and malignant mediastinal lymph nodes, Chin J. Med. Imaging Technology, 2004, 20(5): 673~675
    [6] Li Ruizhen, Study on Portoazygous Shunt Before and After Treatment of Esophageal Varies Using Miniature Ultrasonic Probe and Color Doppler Ultrasonography, Chinese J. Ultrasound Med., 2004, 20(2): 127~130
    [7]孙思予,内镜超声引导下介入技术,纵轴内镜超声诊断及介人技术(第一版),北京:人民卫生出版社,2002
    [8] Frijlink M. E., Goertz D. E., et al., Intravascular ultrasound tissue harmonic imaging in vivo, IEEE trans ultrason Ferroelectr control, 2006, 53(10): 1844~1852
    [9]曹铁生,段云友,多普勒超声诊断学,北京:人民卫生出版社,2004
    [10]王威琪,余建国,近期的医学超声研究,声学技术,1995, 15(2): 91~96
    [11]徐智章,超声诊断发展的新动向,声学技术,1992, 11(1): 22~25
    [12] Yoshida T., Mori M., Nimura Y., et al., Analysis of heart motion with ultrasonic Doppler method and its clinical application, Am. heart J., 1961, 61: 61~75
    [13]魏丽萍,杨瑞英,多普勒组织成像技术及其应用进展,宁夏医学杂志,2003, 25(3): 183~185
    [14]黄晓玲,超声成像新技术的物理声学基础及其应用,中国医学影像材料,2002, 18(5): 498~500
    [15]杜永峰,于铭,微泡超声造影剂材料研究进展,中国功能材料及应用学术会议,2004, 35: 2473~2476
    [16]李洪法,脉冲多普勒血流系统的研制:[硕士学位论文],长春:吉林大学通信工程学院,2004
    [17]鲍静,陈晓冬,温世杰等,医学超声内窥镜下的脉冲多普勒血流检测,现代仪器,2007, 13(7): 21~23
    [18] A. Heimdal, H. Torp, Ultrasound Doppler Measurements of Low Velocity Blood Flow: Limitations Due to Clutter Signals form Vibrating Muscles, IEEE Trans. on Ultrasonics Ferroelectrics and Frequency Control, 1997, 44(4): 873~881
    [19] M. Schlaikjer, J. A. Jensen, Joint Probability Discrimination between Stationary Tissue and Blood Velocity Signals, IEEE Ultrasonics Symposium, 2001: 1397~1400
    [20]金震东,李兆申,消化超声内镜学,北京:科学出版社,2006
    [21]陈彦甫,超声波小动物影像之血流参数计算及应用:[硕士学位论文],台湾:国立台湾大学,2003
    [22]冯若,超声手册,南京:南京大学出版社,2000
    [23]张仁富,高性能TCD的研制:[硕士学位论文],西安:西安电子科技大学,2007
    [24] Hu Changhong, Zhou Qifa, Design and Implementation of High Frequency Ultrasound Pulsed-Wave Doppler Using FPGA, IEEE Transactions on Ultrasonic Ferroelectrics and Frequency Control,2008,55(9): 2109~2111
    [25] S. H. Chang, S. B. Park, G.. H. Cho, Phase-Error-Free Quadrature Sampling Technique in the Ultrasonic B-Scan Imaging System and Its Application to the Synthetic Focusing System, IEEE Trans. on Ultrasonics Ferroelectrics and Frequency Control, 1992, 39(6): 216~223
    [26] Giacomo Bambi, Paolo Fidanzati, Tiziano Morganti, et al., Real-Time Digital Processing of Doppler Ultrasound Signals, IEEE International Conference on Acoustics Speech and signal processing, 2005: 977~980.
    [27]程东彪,高上凯,数字化多深度脉冲波超声多普勒系统的设计与实验研究,中国医学影像技术,2005, 21(8): 1278~1280.
    [28] Mo LYL, Cobbold RSC. Speckle in CW Doppler ultrasound spectra a simulation study, IEEE Trans UFFC, 1986, 33(6): 747~752
    [29]张臣舜,超声多普勒血流动态功率谱分析技术,现代科学与仪器,1996, 4: 39~40
    [30]张良筱,张泾周,马颖颖,超声多普勒血流信号的分析方法,北京生物医学工程,2007, 26(5): 548~558
    [31] Muthuvel Arigovindan, Michael Sühling, Christian Jansen, et al., Full Motion and Flow Field Recovery from Echo Doppler Data, IEEE Transactions on Medical Imaging, 2007, 26(1): 31~45
    [32] B. Liu, Y. Wang, W. Wang, Extracting the Spectrogram Envelop Using theImproved Percentile Method, Tech. Acoust., 1997, 17(1): 9~11
    [33] Loupas T, Peterson RB, Gill RW, Experimental evaluation of velocity and power estimation for ultrasound blood flow imaging, by means of a two-dimensional autocorrelation approach, IEEE Trans UFFC, 1995, 42(4): 689~699
    [34] K. Kaluzynski, Analysis of Application Possibilities of Autoregressive Modeling to Doppler Blood Flow Signal Spectral Analysis, Med. Biol. Eng. Comp, 1987, 25: 373~376
    [35]翟伟,王红莉,王立军,彩色血流成像系统中壁滤波器,中国现代医生,2008, 46(4): 21~24
    [36]翟伟,彩色超声成像系统中壁滤波器的研究:[硕士学位论文],哈尔滨:哈尔滨工业大学,2002
    [37] D. L. Donoho, De-noising by Soft Thresholding, IEEE Trans. On Information Theory, 1995, 41: 613~627
    [38] D. L. Donoho, I. M. Johnstone, Ideal Denoising in an Orthonormal Basis Chosen from a Library of Bases, C. R. Acad. Sci. Paris. A., 1994, 319: 1317~1322
    [39] Sebastian E. Ferrando, Randall Pyke, Ideal denoising for signals in sub-Gaussian noise Applied and Computational Harmonic Analysis, 2008, 24(1): 1~13
    [40] Y. Zhang, Y. Wang, W. Wang, B. Liu, Doppler Ultrasound Signal Denoising Based on Wavelet Frame, IEEE Trans. on Ultrasonics Ferroelectrics and Frequency Control, 2001, 48(7): 709~716
    [41] Y. Zhang, Y. Wang, W. Wang, Denoising quadrature Doppler signals from bi-directional flow using the wavelet frame, IEEE Trans. On Ultrasonics Ferroelectrics and Frequency Control, 2003, 50(5): 561~564
    [42] S. C. Olhede, A. T. Walden, Noise Reduction in Directional Signals Using Multiple Morse Wavelets Illustrated on Quadrature Doppler Ultrasound, IEEE Trans. on Biomedical Engineering, 2003, 50(1): 51~57
    [43]鲍静,医学超声成像系统的编码激励技术研究:[硕士学位论文],天津:天津大学,2007
    [44]祁文康,白净,杨福生等,PVDF超声探头的特性和电学匹配,应用声学,1991, 11(2): 36~39
    [45] ADI Corporation,AD8331 Data Sheet,2006
    [46]付永强,医学超声内窥成像信号接收系统的研究:[硕士学位论文],天津:天津大学,2007
    [47] Linear Corporation,LT1568 Data Sheet, 2007
    [48]杨贵,FPGA在数字信号处理中的应用与研究:[硕士学位论文],长沙:湖南大学,2004
    [49]夏宇闻,Verilog数字系统设计教程,北京:北京航空航天大学出版社,2003
    [50]程东彪,高上凯,数字化多深度脉冲波超声多普勒系统的设计与实验研究,中国医学影像技术,2005, 21(8): 1278~1280
    [51]温世杰,数字式医学超声内窥镜成像系统的研究:[博士学位论文],天津:天津大学,2009
    [52]王诚,吴继华,范丽珍等,Altera FPGA/CPLD设计(基础篇),北京:人民邮电出版社,2005
    [53]程佩青,数字信号处理教程,北京:清华大学出版社,2001
    [54]管吉兴,FFT的FPGA实现,无线电工程,2005, 35(2): 43~46
    [55] FFT MegaCore Function User Guide, Altera, 2008
    [56] B. Liu, Y. Wang, W. Wang, Extracting the Spectrogram Envelop the Improved Percentile Method, Tech. Acoust, 1997, 17(1): 9~11
    [57] K. Kaluzynski, Analysis of Application Possibilities of Autoregressive Modeling to Doppler Blood Flow Signal Spectral Analysis, Med. Biol. Eng.Comp, 1987, 25: 373~376
    [58] B. Liu, Y. Wang, W. Wang, Spectrogram Enhancement Algorithm: a Soft Thresholding-based Approach, Ultrasound in Med. & Biol. 1999, 25(5): 839~846
    [59] David L.Hykes, wayne R. Hedrick, Dale Starhman, Ultrasound physics and instrumentation, St.Louis:Mosby Year Book, c1992
    [60] Steinar B, Hans T., Clutter filter design for ultrasound color flow imaging, IEEE Trans UFFC, 2002, 49(2): 204
    [61] Hu Changhong, Zhou Qifa, Design and Implementation of High Frequency Ultrasound Pulsed-Wave Doppler Using FPGA, IEEE Transactions on Ultrasonic Ferroelectrics and Frequency Control, 2008, 55(9): 2109~2111
    [62] Pan Quan, Zhang Lei, Dai Guanzhong, et a1., Two denoising methods by wavelet transform, IEEE Transactions on Signal Processing, 1999, 47(12): 3401~3406.
    [63] Cohen A, Daubechics I, V P, Wavelets on the interval and fast waveletransforms, Appl Comp. Harm. Anal, 1993, 1(1): 54~81
    [64] Andersson L, Hall N, Jawerth B, et al., Wavelets on closes subsets of the real line. Schumaker L L, Webb Geds. Recents Advance in Wavelet Analysis, Boston: Academic Press, 1994, 1~61.
    [65] Chui C, He W., Compactly supposed tight frames associated with refinable functions, Appl Comp. Harm. Anal, 2000, 8(3): 293~319
    [66] Selesnick I W, Sendur L, Smooth wavelet frames with application to denoising,IEEE Proc Int Conf Acoust, Speech and Signal Processing, Istanbul, Turkey, 2000, l(1): 129~132.
    [67] Donoho D L, Adapting to unknown smoothness via wavelet shrinkage, Amer Statist Assoc, 1995, 90(432): 1200~1224.
    [68] Donoho D L, Johnstone I M, Ideal spatial adaptation by wavelet shrinkage, Biometrika, 1994, 81(3): 425~455.
    [69] I. Daubechies, B. Han, A. Ron, et al., MRA-based constructions of wavelet frames, Appl. Comput. Harmon. Anal., 2003, 14(1): 1~46.
    [70] C. K. Chui, W. He, . St?ckler, Compactly supported tight and sibling frames with maximum vanishing moments, Appl. Comput. Harmon. Anal., 2003, 13(3): 177~283.
    [71] C. Chui, W. He, Compactly supported tight frames associated with refinable functions, Appl. Comp. Harm. Anal., 2000, 8(3): 293~319.
    [72] A. Ron, Z. Shen, Affine systems in L2(Rd): the analysis of the analysis operator, Functional Anal,Appl, 1997, 148: 408~447
    [73] A. Ron, Z. Shen, Compactly supported tight affine spline frames in L2(Rd), Math. Comp., 1998, 67: 191~207.
    [74] Alexander Petukhov, Explicit construction of framelets, Applied and Computational Harmonic Analysis, 2001, 11(2): 313~327.
    [75] I. W. Selesnick, Smooth wavelet tight frames with zero moments, Appl. Comput. Harmon.Anal., 2001, 10(2): 163~181.
    [76] Chang S G, Yu B, Vetterli M, Spatially adaptive wavelet thresholding with context modeling for image denoising, IEEE Transactionson Image Processing, 2000, 9(9): 1522~1531
    [77] Quan Pan, Lei Zhang, Guanzhong Dai, et al., Two Denoising Methods by Wavelet Transform, IEEE Transactions on Signal Processing, 1999, 47(12): 2321~2238
    [78] I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math., 1988, 41(12): 909~996
    [79] Bin Han, Q.T. Jiang, Multiwavelets on the interval, Applied and Computational Harmonic Analysis, 2002, 12(2): 100~127.
    [80] B. Han, On dual wavelets tight frames, Applied Comput. Harmonic Anal., 1994, 7(4): 380~413.
    [81] Zoran Cvetkovic, Martin Vetterli, Oversampled filter banks, IEEE Trans. Signal Processing, 1998, 46(5): 1245~1255.
    [82] Ivan W. Selesnick, Symmetric wavelet tight frames with two generators, Applied and Computational Harmonic Analysis, 2004, 17(2): 211-225
    [83]高协平,周四望,正交平衡对称的区间多小波,中国科学E辑,2005, 35(4):385~404
    [84]彭立中,王海辉,一类光滑小波严格框架的设计,中国科学E辑,2003, 33(8): 681~694
    [85] Gao Xie ping, Cao Chun hang, Minimum energy wavelet frame on the interval, Science in China: Series F, 2008, 51(10): 1547~1562
    [86] Cohen A, Daubechies I, Vial P, Wavelets on the Interval and Fast Wavelet Transforms, Appl Comp. Harm. Anal,1993, 1(1): 54~81.
    [87] I. Daubechies, B. Han, Pairs of dual wavelet frames from any two refinable functions, Constr. Approx., 2004, 20(3):325~352
    [88] Q. Jiang, Parameterizations of masks for tight affine frames with two symmetric/antisymetric generators, Adv. Comput. Math., 2003, 18(2): 247~268.
    [89] A. Petukhov, Symmetric framelets, Constructive Approximation, 2003, 19(2): 309~328
    [90] I. W. Selesnick, L. S’endur, Smooth wavelet frames with application to denoising, IEEE Proc. Int. Conf.Acoust., Speech and Signal Processing, Istanbul, Turkey, 2000, 6(2): 129~132.
    [91] H. B?lcskei, F. Hlawatsch, Oversampled cosine modulated filter banks with perfect reconstruction, IEEE Trans. Circuits Syst. II (Special Issue on Multirate Systems, Filter Banks, Wavelets, and Applications), 1998, 45: 1057~1071
    [92] I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inform. Theory, 1990, 36: 961~1005
    [93] S. Mallat, S. Zhong, Characterization of signals from multiscale edges, IEEE Trans. Pattern Anal. Mach. Intell., 1992, 14: 710~732
    [94]崔锦泰,小波分析导论,西安:西安交通大学出版社,1995
    [95] P. P. Vaidyanathan, Multirate Systems and Filter Banks, Englewood Cliffs, NJ: Prentice-Hall, 1993
    [96] M. Vetterli, J. Kovcevi′c, Wavelets and Subband Coding. Englewood Cliffs, NJ: Prentice-Hall, 1995
    [97] R. Balian, Unprincipe d’incertitude fort en th′eorie du signal on m′ecanique quantique, C. R. Acad. Sci., Paris, 1981, 292: 2
    [98] F. Low, Complete sets of wave packets, in A Passion for Physics-Essays in Honor of Geoffrey Chew, Singapore: World Scientific, 1985, 17–22
    [99] S. Mallat, S. Zhong, Characterization of signals from multiscaleedges, IEEE Trans. Pattern Anal. Mach. Intell., 1992, 14: 710~732
    [100] S. Mallat, Z. Zhang, Matching pursuit with time-frequency dictionaries, IEEE Trans. Signal Processing (Special Issue on Wavelets andSignal Processing),1993, 41: 3397~3415
    [101] S. Mallat,信号处理的小波导引,北京:机械工业出版社,2003
    [102] R. R. Coifman, D. L. Donoho, Translation invariant de-noising, in Wavelets and Statistics, Springer Lecture Notes in Statistics, 1994, 103: 125~150.
    [103] D. L. Donoho, De-noising by Soft Thresholding. IEEE Trans, On Information Theory, 1995, 41: 613~627
    [104] D. Donoho, Adapting to unknown smoothness via wavelet shrinkage, J. Amer. Statist. Assoc., 1995, 90: 432
    [105] H. Y. Gao, Wavelet Shrinkage Denoising Using the Nonnegative Garrote, Comp. Graph. Stat., 1998, 4: 469~488
    [106] D. L. Donoho, I. M. Johnstone, Ideal spatial adaptation by wavelet shrinkage, Biometrika, 1994, 81(3): 425~455
    [107] D. L. Donoho, De-noising by soft-thresholding, IEEE Trans. Inform.Theory, 1995, 41(10): 613~27.
    [108] Marian Kazubek,Wavelet Domain Image Denoising by Thresholding and Wiener Filtering, IEEE Signal Processing Letters, 2003, 10(11): 2361~2368
    [109] Peng-Lang Shui, Image Denoising Algorithm via Doubly Local Wiener Filtering With Directional Windows in Wavelet Domain, IEEE Signal Processing Letters, 2005, 12(10): 516~520
    [110] M. K. Mih?ak, I. Kozinsev, K. Ramchandran, et al., Low-complexity image denoising based on statistical modeling of wavelet coefficients, IEEE Signal Processing Letters, 1999, 6(12): 300~303
    [111] J.R.Holub, Preframe operators,besselian frames .and near rieze bases in Hilbert spaces, Proc.Amer. Math.Soc., 1994, 122: 779~785
    [112] J. J. Benedetto, O. M. Treiber, Wavelet frame: multiresolution analysis and extension principle. In Wavelet Transform and Time-Frquency Signal Analysis, Birkhauser, Boston, 2000.
    [113] J. J. Benedetto, S. Li, The theory of multiresolution analysis frames and applications to filter bands, Appl. Comp. Harmonic Anal., 1998, 5: 389~427.
    [114] H. O. Kim, J. K. Lim., On frame wavelets associated with frame multiresolution analysis, Appl. Comput. Harmon. Anal., 2001, 10: 61~70.
    [115] Benedetto J, Li S.D., The Theory of Multiresolution Analysis Frames and Applications to Filter Banks, Appl. Computer Harmonic Anal., 1998, 5(4): 389~427
    [116] Swel Den W., The Lifting Scheme: a Custom Design Construction of Biorthogonal Wavelets, Appl. And Computer Harmonic Anal., 1992, 40(10): 2462~2482
    [117] Ron A, Shen Z., Construction of Compactly Supproted Affine Frames inL2(Rd), New York: Springer, 1998.
    [118]李建华,李万社,一类小波框架的构造.现代电子信息技术理论与应用,济南:中国电子学会,2005: 872~876
    [119] Vellerli.M, Herley C., wavelets and filter banks: theory and design, IEEE Trans.on signal processing, 1992, 40(9): 2207~2232
    [120]李万社,刘志国,一种有效的小波紧框架设计,西安电子科技大学学报,2006, 33(4): 665~669.
    [121] Y. Wang, P. J. Fish, Arterial Doppler signal simulation by time domain processing, Eur. J. Ultrsound, 1996, 3(1): 71~81
    [122] P. J. Fish, Nonstationarity Broadening in Pulsed Doppler Spectrum Measurements, Ultrasound in Med. & Biol., 1991, 17: 147~155
    [123] A. T. Kerr, J. W. Hunt, A Method for Computer Simulation of Ultrasound Doppler Color Flow Images - I. Theory and Numerical Method, Ultrasound in Medicine & Biology, 1992, 8(10): 861~872
    [124] L. Y. L. Mo, R. S. C. Cobbold, A Stochastic Model of the Backscattered Doppler Ultrasound from Blood, IEEE Trans. On Biomedical Engineering, 1986, 33(1): 20~27

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700