岩石X射线CT信号的分频处理
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摘要
计算机断层成像(Computed Tomography)简称CT,是X射线照相术与复杂的计算机信号处理方法相结合的产物,它在许多科学领域都得到了应用,80年代后期,它被用于观察岩石的内部结构。CT信号通常用CT数表示,并以图形或图像的形式展示。但是由于计算机灰度图像以及人眼分辨能力的限制,需要提高岩石CT图像分辨率,以便能够在直观分析CT信号时得到准确判断。
为了提供高质量清晰的计算机灰度图像,本文从CT机工作原理出发,选择了一组同一试样第一扫描断面的实测CT数据作为研究对象,根据这些CT信号的特点,应用傅立叶变换和小波变换的滤波功能进行分频处理,通过对岩石CT信号进行分解与重构,将CT信号分解为低频信号和高频信号两部分。其中,低频信号反映主体信息,高频信号反映细节信息,总的处理目标是“总体一致,细节突出”。“总体一致”反映了低频信号的可比性,“细节突出”则反映了高频信号的清晰度。通过分频后的CT低频信号对比分析,发现低频信号之间具有一致性,分频之后的高频信号图像分辨率比分频前有所提高,并与裂纹有明显的对应关系。
分频处理表明,CT低频信号是一种确定性信号,相互之间具有可比性,反映了岩石试样内部结构的总体特征;CT高频信号则表现为一种随机信号,它反映了岩石试样受外荷载作用过程中岩石内部密度的变化和CT机引起的随机干扰。通过分频处理显示两种CT图像,可显著提高图像分辨率。
为了获得试样在加荷过程中其内部结构的变化,采用了同心环和裂隙域两种统计方案对高频CT信号进行数据统计,统计表明,应用两种方法得到的统计结果具有相似的规律,说明利用傅立叶或小波方法进行分频处理结果具有可比性,对提高CT信号图像的分辨率有重要作用。
CT is the abbreviation of computer Tomography, which combined the X ray and the complicated computer signals processing method. CT has been applied in many fields of science, and in the late of 1980s, it is used to observe the inner structure of rock block. CT signals are usually expressed as CT number and displayed by graphic or image. However, because of the restrictions of computer gray image and the eyes of man's distinguish ability, we need to improve the image resolution of the CT, in order to make an accurate judgement when we have a direct analysis of the CT signals.
In order to provide high-quality and clear computer gray images, on the basis of the principle of CT machine, this paper selected a group of the same samples of the first section of the measured CT scan data as the research object, according to the characteristics of these CT signals, the filtering function of Fourier Transform and wavelet transform were applied to divide the frequency, through the decomposition and reconstruction of CT signals, it is divided into low-frequency signals and high-frequency in two parts. The low-frequency signals reflect the main information, high-frequency signals reflect the details, and the overall goal is to deal with "general agreement, the details highlighted." "The overall agreement" reflects the low-frequency signals' comparability, "the details highlighted" reflects the clarity of high-frequency signal. Through the comparative analysis of low-frequency of the CT signals, we found that the consistency exists in low-frequency signals, after frequency demultiplication, the image resolution of high frequency signal increased more than before, and it was obviously matched with the cracks.
Frequency separation shows that the low-frequency signal of CT is a certain signal, comparable between each other and it reflects the overall characteristic of the inner structure of the rock sample, the high-frequency signal is a random signal, it reflects when the rock samples on the load, the changes of density in rock and random interference caused by CT machines. Through illustration of a two-CT image showed that it can improve the image resolution significantly.
In order to obtain internal structure changes of samples in the loading process, we employed concentric ring and fractured domain to make statistics of the high frequency signal, statistics show that the two methods have similar results of the law, and have close relations with the selection of regional, this indicates that it is feasible to use Fourier or Wavelet methods to separate frequency, in order to promote the resolution of the CT images.
为了提供高质量清晰的计算机灰度图像,本文从CT机工作原理出发,选择了一组同一试样第一扫描断面的实测CT数据作为研究对象,根据这些CT信号的特点,应用傅立叶变换和小波变换的滤波功能进行分频处理,通过对岩石CT信号进行分解与重构,将CT信号分解为低频信号和高频信号两部分。其中,低频信号反映主体信息,高频信号反映细节信息,总的处理目标是“总体一致,细节突出”。“总体一致”反映了低频信号的可比性,“细节突出”则反映了高频信号的清晰度。通过分频后的CT低频信号对比分析,发现低频信号之间具有一致性,分频之后的高频信号图像分辨率比分频前有所提高,并与裂纹有明显的对应关系。
分频处理表明,CT低频信号是一种确定性信号,相互之间具有可比性,反映了岩石试样内部结构的总体特征;CT高频信号则表现为一种随机信号,它反映了岩石试样受外荷载作用过程中岩石内部密度的变化和CT机引起的随机干扰。通过分频处理显示两种CT图像,可显著提高图像分辨率。
为了获得试样在加荷过程中其内部结构的变化,采用了同心环和裂隙域两种统计方案对高频CT信号进行数据统计,统计表明,应用两种方法得到的统计结果具有相似的规律,说明利用傅立叶或小波方法进行分频处理结果具有可比性,对提高CT信号图像的分辨率有重要作用。
CT is the abbreviation of computer Tomography, which combined the X ray and the complicated computer signals processing method. CT has been applied in many fields of science, and in the late of 1980s, it is used to observe the inner structure of rock block. CT signals are usually expressed as CT number and displayed by graphic or image. However, because of the restrictions of computer gray image and the eyes of man's distinguish ability, we need to improve the image resolution of the CT, in order to make an accurate judgement when we have a direct analysis of the CT signals.
In order to provide high-quality and clear computer gray images, on the basis of the principle of CT machine, this paper selected a group of the same samples of the first section of the measured CT scan data as the research object, according to the characteristics of these CT signals, the filtering function of Fourier Transform and wavelet transform were applied to divide the frequency, through the decomposition and reconstruction of CT signals, it is divided into low-frequency signals and high-frequency in two parts. The low-frequency signals reflect the main information, high-frequency signals reflect the details, and the overall goal is to deal with "general agreement, the details highlighted." "The overall agreement" reflects the low-frequency signals' comparability, "the details highlighted" reflects the clarity of high-frequency signal. Through the comparative analysis of low-frequency of the CT signals, we found that the consistency exists in low-frequency signals, after frequency demultiplication, the image resolution of high frequency signal increased more than before, and it was obviously matched with the cracks.
Frequency separation shows that the low-frequency signal of CT is a certain signal, comparable between each other and it reflects the overall characteristic of the inner structure of the rock sample, the high-frequency signal is a random signal, it reflects when the rock samples on the load, the changes of density in rock and random interference caused by CT machines. Through illustration of a two-CT image showed that it can improve the image resolution significantly.
In order to obtain internal structure changes of samples in the loading process, we employed concentric ring and fractured domain to make statistics of the high frequency signal, statistics show that the two methods have similar results of the law, and have close relations with the selection of regional, this indicates that it is feasible to use Fourier or Wavelet methods to separate frequency, in order to promote the resolution of the CT images.
引文
[1]周光湖.计算机断层摄影原理及应用[M].四川:成都电讯工程学院,1986
[2]朱翠玲,赵斌,吴恩惠主编.现代医学影像学[M].济南:山东科学技术出版社,2000
[3]罗述谦,周果宏编著.医学图象处理与分析[M].北京:科学出版社,2003
[4]杨更社.岩体损伤力学特性及细观损伤的CT识别[D].西安:西安理工大学,1995.
[5]葛修润,任建喜,蒲毅彬等.岩石疲劳损伤扩展规律CT细观分析初探[J].岩土工程学报,2001,23(2):191-195.
[6]丁玉美,高西全.数字信号处理[M].西安:西安电子科技大学出版社,2001
[7]Rafale C Gonzalez,Richard Woods著.数字图象处理[M].北京:电子工业出版社,2004
[8]屠耀元.层析摄影与CT技术[J].无损检测,1992,14(10):37-42.
[9]赫尔曼,严洪范.由投影重建图像-CT的理论基础[M].北京:科学出版社,1985.
[10]屈庆春,基于beamlet的多尺度图象分析及其在CT图象处理中的应用[D].济南:山东大学,2005
[11]Raynaud S,Fabre D,Mazerolle F,et al.Analysis of the internal structure of rocks and characterization of mechanical deformation by a nondestructive method:X ray tomodensitometry[J].Tecto nop hysics,1989,159:149-159.
[12]Kawakata H,Cho A,Kiyama T,Yanagidani T,Kusunose K,Shimada M.Three-dimensional observations of faulting process in Westerly granite under uniaxial and triaxial conditions by X-ray CT scan.Techonophysics,1999,313:293-305
[13]Ron C K,Wong.Mobilized Strength Components of Athab-asca Oil Sand in Triaxial Compression[J].In:Can Geotech J,1999,36:718-735.
[14]Ueta K,Tani K,Kato T.Computerized X-ray tomography analysis of three-dimensional fault geometries in basement-induced wrench faulting[J].Engineering Geology,2000 56:197-210
[15]杨更社,岩石材料损伤变量与CT数间的关系分析[J].力学与实践,1998,20(4):47-49.
[16]杨更社,谢定义,张长庆,蒲毅彬.岩石损伤单轴受力状态本构关系的CT识别[J].岩土力学,1997,10(2):29-32.
[17]YANG Geng-she.CT identification of the damage co-nstitutive relation of rock under the uniaxial stresscondition[A].Int.Symp.on Strength theory:Appli-cation Development and Prospects for 21stCentury[C].Xi'an,China:Sep.,1998.850-857.
[18]杨更社,谢定义,张长庆,蒲毅彬.岩石损伤CT数的定量分析[J].岩石力学与工程学报,1998,17(3):279-285.
[19]葛修润,任建喜,蒲毅彬等.煤岩三轴细观损伤演化规律的CT动态试验[J].岩石力学与工程学报,1999,18(5):497-502.
[20]仵彦卿,丁卫华,蒲毅彬,等压缩条件下岩石密度损伤增量的CT动态观[J].自然科学进展,2000.(9):830-835
[21]丁卫华,仵彦卿,蒲毅彬等.受力岩石密度损伤增量及其数字图像[J].西安理工大学学报,2000,16(1):61-64.
[22]丁卫华,岩石内部破裂过程的CT动态监测[D].西安:西安理工大学,2001
[23]庄天戈.CT原理与算法[M].上海:上海交通大学出版社,1999
[24]叶鸿瑾,基于小波变换的医学图象处理研究[D].太原:太原理工大学,2002
[25]裴作升,各代X-CT扫描机的优缺点[J].医疗卫生设备,2005,26(2):1-2
[26]章毓晋.图像处理和分析[M].北京:清华大学出版社,1999
[27]刘彦文,混凝土力学行为的CT研究[D].西安:西安理工大学,2007
[28]于雷,计算机断层扫描技术在木材检测中的应用[D].哈尔滨:东北林业大学,2007
[29]高欣,新型迭代图像重建算法的理论研究和实现[D].杭州:浙江大学,2004,11-13
[30]赵荣椿.数字图像处理导论[M].西安:西北工业大学出版社,1995.167-188
[31]姚敏.数字图象处理[M].北京:机械工业出版社,2006
[32]Ludwig D.The Radon transform on Euclidean space[J].Comm Pure Appl Math,1966
[33]陈书海,傅录祥,实用数字图像处理[M].北京:科学出版社2005.317-343
[34]王新跃,工业CT不完全投影及偏置扫描重构研究[D].太原:华北工学院,2003
[35]庞彦伟,工业CT技术研究[D].太原:华北工学院,2001
[36]陈书海,傅录祥.实用数字图像处理[M].北京:科学出版社2005.317-343
[37]李想.CT图像的应用研究[D].哈尔滨:哈尔滨工程大学,2004
[38]仵彦卿,丁卫华,蒲毅彬,等压缩条件下岩石密度损伤增量的CT动态观[J].自然科学进展,2000.(9):830-835
[39]霍修坤.锥束CT直接三维成像算法研究[D].合肥:安徽大学,2005
[40]胡广书.数字信号处理——理论、算法与实现[M].第二版.北京:清华大学出版社,2003
[41]Kenneth R Castleman著.数字图象处理[M].北京:电子工业出版社,1998
[42]崔金刚,图象处理技术在木材检测方面的应用[D].哈尔滨:东北林业大学,2007
[43]朱虹.数字图像处理基础[M].北京:科学出版社,2005
[44]王晓丹,吴祟明.基于Matlab的系统分析与设计——图像处理[M].西安:西安电子科技大学出版社,2000
[45]吴大正,信号与线性系统[M].北京:高等教育出版社,1998,116-193
[46]毛黎明,岩石材料X射线CT图象伪影研究[D].西安:西安理工大学,2007
[47]陈武凡,小波分析及其在图象处理中的应用[M].北京:科学出版社,2002
[48]杨福生,小波变换的工程分析与应用[M].北京:科学出版社,2000
[49]李廷春,三维裂隙扩展的CT试验及理论分析研究[D].武汉:中国科学院武汉岩土力学研究所.2005
[2]朱翠玲,赵斌,吴恩惠主编.现代医学影像学[M].济南:山东科学技术出版社,2000
[3]罗述谦,周果宏编著.医学图象处理与分析[M].北京:科学出版社,2003
[4]杨更社.岩体损伤力学特性及细观损伤的CT识别[D].西安:西安理工大学,1995.
[5]葛修润,任建喜,蒲毅彬等.岩石疲劳损伤扩展规律CT细观分析初探[J].岩土工程学报,2001,23(2):191-195.
[6]丁玉美,高西全.数字信号处理[M].西安:西安电子科技大学出版社,2001
[7]Rafale C Gonzalez,Richard Woods著.数字图象处理[M].北京:电子工业出版社,2004
[8]屠耀元.层析摄影与CT技术[J].无损检测,1992,14(10):37-42.
[9]赫尔曼,严洪范.由投影重建图像-CT的理论基础[M].北京:科学出版社,1985.
[10]屈庆春,基于beamlet的多尺度图象分析及其在CT图象处理中的应用[D].济南:山东大学,2005
[11]Raynaud S,Fabre D,Mazerolle F,et al.Analysis of the internal structure of rocks and characterization of mechanical deformation by a nondestructive method:X ray tomodensitometry[J].Tecto nop hysics,1989,159:149-159.
[12]Kawakata H,Cho A,Kiyama T,Yanagidani T,Kusunose K,Shimada M.Three-dimensional observations of faulting process in Westerly granite under uniaxial and triaxial conditions by X-ray CT scan.Techonophysics,1999,313:293-305
[13]Ron C K,Wong.Mobilized Strength Components of Athab-asca Oil Sand in Triaxial Compression[J].In:Can Geotech J,1999,36:718-735.
[14]Ueta K,Tani K,Kato T.Computerized X-ray tomography analysis of three-dimensional fault geometries in basement-induced wrench faulting[J].Engineering Geology,2000 56:197-210
[15]杨更社,岩石材料损伤变量与CT数间的关系分析[J].力学与实践,1998,20(4):47-49.
[16]杨更社,谢定义,张长庆,蒲毅彬.岩石损伤单轴受力状态本构关系的CT识别[J].岩土力学,1997,10(2):29-32.
[17]YANG Geng-she.CT identification of the damage co-nstitutive relation of rock under the uniaxial stresscondition[A].Int.Symp.on Strength theory:Appli-cation Development and Prospects for 21stCentury[C].Xi'an,China:Sep.,1998.850-857.
[18]杨更社,谢定义,张长庆,蒲毅彬.岩石损伤CT数的定量分析[J].岩石力学与工程学报,1998,17(3):279-285.
[19]葛修润,任建喜,蒲毅彬等.煤岩三轴细观损伤演化规律的CT动态试验[J].岩石力学与工程学报,1999,18(5):497-502.
[20]仵彦卿,丁卫华,蒲毅彬,等压缩条件下岩石密度损伤增量的CT动态观[J].自然科学进展,2000.(9):830-835
[21]丁卫华,仵彦卿,蒲毅彬等.受力岩石密度损伤增量及其数字图像[J].西安理工大学学报,2000,16(1):61-64.
[22]丁卫华,岩石内部破裂过程的CT动态监测[D].西安:西安理工大学,2001
[23]庄天戈.CT原理与算法[M].上海:上海交通大学出版社,1999
[24]叶鸿瑾,基于小波变换的医学图象处理研究[D].太原:太原理工大学,2002
[25]裴作升,各代X-CT扫描机的优缺点[J].医疗卫生设备,2005,26(2):1-2
[26]章毓晋.图像处理和分析[M].北京:清华大学出版社,1999
[27]刘彦文,混凝土力学行为的CT研究[D].西安:西安理工大学,2007
[28]于雷,计算机断层扫描技术在木材检测中的应用[D].哈尔滨:东北林业大学,2007
[29]高欣,新型迭代图像重建算法的理论研究和实现[D].杭州:浙江大学,2004,11-13
[30]赵荣椿.数字图像处理导论[M].西安:西北工业大学出版社,1995.167-188
[31]姚敏.数字图象处理[M].北京:机械工业出版社,2006
[32]Ludwig D.The Radon transform on Euclidean space[J].Comm Pure Appl Math,1966
[33]陈书海,傅录祥,实用数字图像处理[M].北京:科学出版社2005.317-343
[34]王新跃,工业CT不完全投影及偏置扫描重构研究[D].太原:华北工学院,2003
[35]庞彦伟,工业CT技术研究[D].太原:华北工学院,2001
[36]陈书海,傅录祥.实用数字图像处理[M].北京:科学出版社2005.317-343
[37]李想.CT图像的应用研究[D].哈尔滨:哈尔滨工程大学,2004
[38]仵彦卿,丁卫华,蒲毅彬,等压缩条件下岩石密度损伤增量的CT动态观[J].自然科学进展,2000.(9):830-835
[39]霍修坤.锥束CT直接三维成像算法研究[D].合肥:安徽大学,2005
[40]胡广书.数字信号处理——理论、算法与实现[M].第二版.北京:清华大学出版社,2003
[41]Kenneth R Castleman著.数字图象处理[M].北京:电子工业出版社,1998
[42]崔金刚,图象处理技术在木材检测方面的应用[D].哈尔滨:东北林业大学,2007
[43]朱虹.数字图像处理基础[M].北京:科学出版社,2005
[44]王晓丹,吴祟明.基于Matlab的系统分析与设计——图像处理[M].西安:西安电子科技大学出版社,2000
[45]吴大正,信号与线性系统[M].北京:高等教育出版社,1998,116-193
[46]毛黎明,岩石材料X射线CT图象伪影研究[D].西安:西安理工大学,2007
[47]陈武凡,小波分析及其在图象处理中的应用[M].北京:科学出版社,2002
[48]杨福生,小波变换的工程分析与应用[M].北京:科学出版社,2000
[49]李廷春,三维裂隙扩展的CT试验及理论分析研究[D].武汉:中国科学院武汉岩土力学研究所.2005