1、Technical EnglishTechnical EnglishFor Information and Communication Engineering 2024/4/16Unit SevenComputerized Tomographic Imaging 概述n n计算机层析成像的基本原理计算机层析成像的基本原理计算机层析成像的基本原理计算机层析成像的基本原理n nHounsfieldHounsfield的发明及其意义的发明及其意义的发明及其意义的发明及其意义n nX X射线射线射线射线CTCT和衍射和衍射和衍射和衍射CTCTn nCTCT技术的应用领域技术的应用领域技术的应用领域技术
2、的应用领域2tomographytomography断层成像术断层成像术断层成像术断层成像术transmissiontransmission透射透射透射透射reflectionreflection反射反射反射反射diagnosticdiagnostic诊断诊断诊断诊断unprecedentedunprecedented前所未有的，空前的前所未有的，空前的前所未有的，空前的前所未有的，空前的attenuationattenuation衰减衰减衰减衰减coefficientcoefficient系数系数系数系数radioisotoperadioisotope放射性同位素放射性同位素放射性同位素放射
3、性同位素resonanceresonance共振共振共振共振lend oneself tolend oneself to有助于，适宜于有助于，适宜于有助于，适宜于有助于，适宜于boreholeborehole钻孔钻孔钻孔钻孔celestialcelestial天空的天空的天空的天空的integralintegral积分积分积分积分diffractdiffract衍射，绕射衍射，绕射衍射，绕射衍射，绕射cross-sectionalcross-sectional断面的，截面的断面的，截面的断面的，截面的断面的，截面的3breakneckbreakneck极快的，很危险的极快的，很危险的极快的，很
4、危险的极快的，很危险的algebraicalgebraic代数的代数的代数的代数的backprojectionbackprojection反向投影反向投影反向投影反向投影unambiguousunambiguous不模糊的，不含糊的不模糊的，不含糊的不模糊的，不含糊的不模糊的，不含糊的anatomicalanatomical解剖学的解剖学的解剖学的解剖学的cylindercylinder柱体，圆柱柱体，圆柱柱体，圆柱柱体，圆柱isotopeisotope同位素同位素同位素同位素viz.viz.(拉丁语拉丁语拉丁语拉丁语videlicetvidelicet)就是说（可读就是说（可读就是说（可读就
5、是说（可读namelynamely）scatterscatter散射散射散射散射inhomogeneityinhomogeneity不均匀性不均匀性不均匀性不均匀性refractive indexrefractive index折射率折射率折射率折射率variationvariation变种变种变种变种avalancheavalanche雪崩雪崩雪崩雪崩bibliographybibliography参考书目参考书目参考书目参考书目citecite引述，引用引述，引用引述，引用引述，引用4通过从许多不同方向照射物体，根据透通过从许多不同方向照射物体，根据透通过从许多不同方向照射物体，根据透通过
6、从许多不同方向照射物体，根据透射或反射的数据对物体断面成像射或反射的数据对物体断面成像射或反射的数据对物体断面成像射或反射的数据对物体断面成像它使医生能以前所未有的精度看到体它使医生能以前所未有的精度看到体它使医生能以前所未有的精度看到体它使医生能以前所未有的精度看到体内的器官而对病人十分安全。内的器官而对病人十分安全。内的器官而对病人十分安全。内的器官而对病人十分安全。TomographyTomography refers to refers to the cross-sectional imaging of an object the cross-sectional imaging of
7、an object from either transmission or reflection data collected by from either transmission or reflection data collected by illuminating the object from many different directionsilluminating the object from many different directions.The.The impact of this technique in diagnostic medicine has been im
8、pact of this technique in diagnostic medicine has been revolutionary,since revolutionary,since it has enabled doctors to view internal it has enabled doctors to view internal organs with unprecedented precision and safety to the patient.organs with unprecedented precision and safety to the patient.U
9、nit 7Unit 75后来利用放射性同位素、超声、磁共振后来利用放射性同位素、超声、磁共振后来利用放射性同位素、超声、磁共振后来利用放射性同位素、超声、磁共振也成功地获得了医学图像，在每一种情也成功地获得了医学图像，在每一种情也成功地获得了医学图像，在每一种情也成功地获得了医学图像，在每一种情况下用不同的参数成像。况下用不同的参数成像。况下用不同的参数成像。况下用不同的参数成像。The first medical application utilized x-rays for forming The first medical application utilized x-rays for
10、forming images of tissues based on their x-ray attenuation coefficient.images of tissues based on their x-ray attenuation coefficient.More recently,however,medical imaging has also been More recently,however,medical imaging has also been successfully accomplished with radioisotopes,ultrasound,and su
11、ccessfully accomplished with radioisotopes,ultrasound,and magnetic resonance;the imaged parameter being different in magnetic resonance;the imaged parameter being different in each case.each case.Unit 7Unit 76还有大量的非医学应用也可使还有大量的非医学应用也可使还有大量的非医学应用也可使还有大量的非医学应用也可使用计算机层析成像方法。用计算机层析成像方法。用计算机层析成像方法。用计算机层析
12、成像方法。1.1.通过钻孔成像测绘地下资源通过钻孔成像测绘地下资源通过钻孔成像测绘地下资源通过钻孔成像测绘地下资源2.2.无损检测中断面成像的某些特殊案例无损检测中断面成像的某些特殊案例无损检测中断面成像的某些特殊案例无损检测中断面成像的某些特殊案例3.3.确定天球面上的亮度分布确定天球面上的亮度分布确定天球面上的亮度分布确定天球面上的亮度分布4.4.电子显微镜三维成像电子显微镜三维成像电子显微镜三维成像电子显微镜三维成像 There are numerous non-medical imaging applications which There are numerous non-medic
13、al imaging applications which lend themselves tolend themselves to the methods of computerized the methods of computerized tomographytomography.Researchers have already applied this methodology to Researchers have already applied this methodology to the the mapping ofmapping of underground resources
14、 via cross-borehole underground resources via cross-borehole imaging,imaging,some specialized cases ofsome specialized cases of cross-sectional imaging for cross-sectional imaging for nondestructive testing,nondestructive testing,the determination ofthe determination of the brightness the brightness
15、 distribution over a celestial sphere,distribution over a celestial sphere,and three-dimensional and three-dimensional imagingimaging with electron microscopy.with electron microscopy.1 1 Unit 7Unit 7lend themselves tolend themselves to有助于，适宜于有助于，适宜于有助于，适宜于有助于，适宜于7某一角度的投影是图像在该角度所某一角度的投影是图像在该角度所某一角度的
16、投影是图像在该角度所某一角度的投影是图像在该角度所定义的方向上的积分定义的方向上的积分定义的方向上的积分定义的方向上的积分 Fundamentally,Fundamentally,tomographictomographic imaging deals with imaging deals with reconstructing an image from its projections.In the strict reconstructing an image from its projections.In the strict sense of the word,sense of the
17、word,a projection at a given angle is the integral a projection at a given angle is the integral of the image in the direction specified by that angleof the image in the direction specified by that angle,as,as illustrated in illustrated in Figure 7.1Figure 7.1.Unit 7Unit 78在宽泛的意义上在宽泛的意义上在宽泛的意义上在宽泛的意
18、义上 若辐射源是衍射性的如超声波或微波，若辐射源是衍射性的如超声波或微波，若辐射源是衍射性的如超声波或微波，若辐射源是衍射性的如超声波或微波，可使用可使用可使用可使用“衍射投影衍射投影衍射投影衍射投影”一词。一词。一词。一词。However,However,in a loose sensein a loose sense,projection means the information,projection means the information derived from the transmitted energies,when an object is derived from the
19、 transmitted energies,when an object is illuminated from a particular angle;illuminated from a particular angle;the phrase“diffracted the phrase“diffracted projection”may be used when energy sources are diffracting,projection”may be used when energy sources are diffracting,as is the case with ultras
20、ound and microwaves.as is the case with ultrasound and microwaves.2 2 Unit 7Unit 79对于如何根据投影数据重建图象这一问题对于如何根据投影数据重建图象这一问题对于如何根据投影数据重建图象这一问题对于如何根据投影数据重建图象这一问题的解要追溯到的解要追溯到的解要追溯到的解要追溯到19171917年年年年RadonRadon的论文的论文的论文的论文 当前在断层成像方面令人激动的成就源自当前在断层成像方面令人激动的成就源自当前在断层成像方面令人激动的成就源自当前在断层成像方面令人激动的成就源自HounsfieldHoun
21、sfield发明的发明的发明的发明的X X光光光光CTCT扫描，他因此项发扫描，他因此项发扫描，他因此项发扫描，他因此项发明而于明而于明而于明而于19791979年获得了诺贝尔奖。年获得了诺贝尔奖。年获得了诺贝尔奖。年获得了诺贝尔奖。Although,from a purely mathematical standpoint,Although,from a purely mathematical standpoint,the the solution to the problem of how to reconstruct a function from solution to the pro
22、blem of how to reconstruct a function from its projections dates back to the paper by Radon in 1917its projections dates back to the paper by Radon in 1917,the the current excitement in current excitement in tomographictomographic imaging originated with imaging originated with HounsfieldHounsfields
23、 invention of the x-ray computed s invention of the x-ray computed tomographictomographic scanner for which he received a Nobel prize in 1979.scanner for which he received a Nobel prize in 1979.3 3Unit 7Unit 710有可能得到精度达千分之一的有可能得到精度达千分之一的有可能得到精度达千分之一的有可能得到精度达千分之一的高质量断面图象高质量断面图象高质量断面图象高质量断面图象 投影数据并未严格
24、满足有效实现重投影数据并未严格满足有效实现重投影数据并未严格满足有效实现重投影数据并未严格满足有效实现重建算法赖以成立的理论模型建算法赖以成立的理论模型建算法赖以成立的理论模型建算法赖以成立的理论模型 He shared the prize with Allan He shared the prize with Allan CormackCormack who independently who independently discovered some of the algorithms.His invention showed that discovered some of the alg
25、orithms.His invention showed that it is possible to compute high-quality cross-sectional images it is possible to compute high-quality cross-sectional images with an accuracy now reaching one part in a thousandwith an accuracy now reaching one part in a thousand in spite in spite of the fact that of
26、 the fact that the projection data do not strictly satisfy the the projection data do not strictly satisfy the theoretical models underlying the efficiently theoretical models underlying the efficiently implementableimplementable reconstruction algorithms.reconstruction algorithms.4 4 Unit 7Unit 711
27、仍然可获得非常精确的图像仍然可获得非常精确的图像仍然可获得非常精确的图像仍然可获得非常精确的图像 His invention also showed that it is possible to process a very His invention also showed that it is possible to process a very large number of measurements(now approaching a million large number of measurements(now approaching a million for the case
28、of x-ray for the case of x-ray tomographytomography)with fairly complex)with fairly complex mathematical operations,and mathematical operations,and still get an image that is still get an image that is incredibly accurateincredibly accurate.Unit 7Unit 712可以说自从可以说自从可以说自从可以说自从HounsfieldHounsfield的发明以来
29、，的发明以来，的发明以来，的发明以来，X X光光光光CTCT成像技术成像技术成像技术成像技术的改进在很大程度上要归功于重建算法方面的发展。的改进在很大程度上要归功于重建算法方面的发展。的改进在很大程度上要归功于重建算法方面的发展。的改进在很大程度上要归功于重建算法方面的发展。重建大小为重建大小为重建大小为重建大小为8080 8080的噪声颇大的噪声颇大的噪声颇大的噪声颇大的图像，精度为百分之一的图像，精度为百分之一的图像，精度为百分之一的图像，精度为百分之一 It is fair to say that the breakneck pace at which x-ray It is fair
30、to say that the breakneck pace at which x-ray computed computed tomographytomography images improved after images improved after HounsfieldHounsfields s invention was in large measure owing to the developments invention was in large measure owing to the developments that were made in reconstruction
31、algorithms.that were made in reconstruction algorithms.5 5 HounsfieldHounsfield used algebraic techniques,and was able used algebraic techniques,and was able to reconstruct noisy to reconstruct noisy looking 80looking 80 80 images with an accuracy of one part in a 80 images with an accuracy of one p
32、art in a hundredhundred.Unit 7Unit 713随后是卷积反向投影算法在这随后是卷积反向投影算法在这随后是卷积反向投影算法在这随后是卷积反向投影算法在这种成像中的应用种成像中的应用种成像中的应用种成像中的应用 This was followed by the application of convolution This was followed by the application of convolution backprojectionbackprojection algorithms algorithms,first developed by,first d
33、eveloped by RamachandranRamachandran and and LakshminarayananLakshminarayanan and later popularized by and later popularized by SheppShepp and and Logan,Logan,to this type of imagingto this type of imaging.These later algorithms.These later algorithms considerably reduced the processing time for rec
34、onstruction,considerably reduced the processing time for reconstruction,and the image produced was numerically more accurate.and the image produced was numerically more accurate.Unit 7Unit 714X X射线层析成像扫描装置的制造商开始生产能射线层析成像扫描装置的制造商开始生产能射线层析成像扫描装置的制造商开始生产能射线层析成像扫描装置的制造商开始生产能重建重建重建重建256256 256256和和和和5125
35、12 512512图像的系统，图像的系统，图像的系统，图像的系统，所形成的形态细节清晰可辩，并与解剖结果完全一致，所形成的形态细节清晰可辩，并与解剖结果完全一致，所形成的形态细节清晰可辩，并与解剖结果完全一致，所形成的形态细节清晰可辩，并与解剖结果完全一致，在这一意义上这些图像几乎达到了照相术上完美的程度。在这一意义上这些图像几乎达到了照相术上完美的程度。在这一意义上这些图像几乎达到了照相术上完美的程度。在这一意义上这些图像几乎达到了照相术上完美的程度。As a result,As a result,commercial manufacturers of x-ray commercial ma
36、nufacturers of x-ray tomographictomographic scanners started building systems capable of reconstructing scanners started building systems capable of reconstructing 256256 256 and 512256 and 512 512 images512 images that were that were almost almost photographically perfect(in the sense that the morp
37、hological photographically perfect(in the sense that the morphological detail produced was unambiguous and in perfect agreement detail produced was unambiguous and in perfect agreement with the anatomical features)with the anatomical features).Unit 7Unit 715在在在在X X射线射线射线射线CTCT取得巨大成功取得巨大成功取得巨大成功取得巨大成
38、功的情况下的情况下的情况下的情况下 近年来更多的注意力集中于将近年来更多的注意力集中于将近年来更多的注意力集中于将近年来更多的注意力集中于将这一成像技术进行扩展这一成像技术进行扩展这一成像技术进行扩展这一成像技术进行扩展 Given the enormous success of x-ray computed Given the enormous success of x-ray computed tomographytomography,it,it is not surprising that is not surprising that in recent years much atten
39、tion has been in recent years much attention has been focused on extending this image formation techniquefocused on extending this image formation technique to to nuclear medicine and magnetic resonance on one hand;and nuclear medicine and magnetic resonance on one hand;and ultrasound and microwaves
40、 on the other.ultrasound and microwaves on the other.Unit 7Unit 716在这两个领域都可以建立起基于图在这两个领域都可以建立起基于图在这两个领域都可以建立起基于图在这两个领域都可以建立起基于图7.17.1中这中这中这中这类投影来重建图像的问题。类投影来重建图像的问题。类投影来重建图像的问题。类投影来重建图像的问题。在于重建人体内放射性同位素在于重建人体内放射性同位素在于重建人体内放射性同位素在于重建人体内放射性同位素分布的断面图像分布的断面图像分布的断面图像分布的断面图像 In nuclear medicine,our intere
41、st is In nuclear medicine,our interest is in reconstructing a cross-in reconstructing a cross-sectional image of radioactive isotope distributions within sectional image of radioactive isotope distributions within the human bodythe human body;and in imaging with magnetic resonance;and in imaging wit
42、h magnetic resonance we wish to reconstruct the magnetic properties of the object.we wish to reconstruct the magnetic properties of the object.In both these areas,the problem can be set up as In both these areas,the problem can be set up as reconstructing an image from its projections of the type re
43、constructing an image from its projections of the type shown in shown in Figure 7.1Figure 7.1.Unit 7Unit 717用超声波和微波作能源时情况用超声波和微波作能源时情况用超声波和微波作能源时情况用超声波和微波作能源时情况有所不同有所不同有所不同有所不同 尽管其目的和尽管其目的和尽管其目的和尽管其目的和X X射线射线射线射线CTCT相同，即重建某一相同，即重建某一相同，即重建某一相同，即重建某一参数（例如衰减系数）的断层图像参数（例如衰减系数）的断层图像参数（例如衰减系数）的断层图像参数（例如衰减
44、系数）的断层图像This is not the case when ultrasound and microwaves are used This is not the case when ultrasound and microwaves are used as energy sourcesas energy sources,although the aim is the same as with X-although the aim is the same as with X-rays,viz.,to reconstruct the cross-sectional image of,say
45、,the rays,viz.,to reconstruct the cross-sectional image of,say,the attenuation coefficientattenuation coefficient.6 6 X-rays are non-diffracting,i.e.,they X-rays are non-diffracting,i.e.,they travel in straight lines,whereas microwaves and ultrasound travel in straight lines,whereas microwaves and u
46、ltrasound are diffracting.are diffracting.Unit 7Unit 718在某些条件下在某些条件下在某些条件下在某些条件下 这些条件是：场的不均匀范围远大于波这些条件是：场的不均匀范围远大于波这些条件是：场的不均匀范围远大于波这些条件是：场的不均匀范围远大于波长，并用折射率作为成像参数长，并用折射率作为成像参数长，并用折射率作为成像参数长，并用折射率作为成像参数When an object is illuminated with a diffracting source,the When an object is illuminated with a di
47、ffracting source,the wave field is scattered in practically all directions,although wave field is scattered in practically all directions,although under certain conditionsunder certain conditions one might be able to get away with one might be able to get away with the assumption of straight line pr
48、opagation;the assumption of straight line propagation;these conditions these conditions being satisfied when the being satisfied when the inhomogeneitiesinhomogeneities are much larger than are much larger than the wavelength and when the imaging parameter is the the wavelength and when the imaging
49、parameter is the refractive index.refractive index.7 7 Unit 7Unit 7当使用衍射源照射物体时，尽管当场的不均匀范围当使用衍射源照射物体时，尽管当场的不均匀范围当使用衍射源照射物体时，尽管当场的不均匀范围当使用衍射源照射物体时，尽管当场的不均匀范围远大于波长并用折射率作为成像参数时，可以满足远大于波长并用折射率作为成像参数时，可以满足远大于波长并用折射率作为成像参数时，可以满足远大于波长并用折射率作为成像参数时，可以满足于直线传播的假设，波实际上是向四面八方散射的。于直线传播的假设，波实际上是向四面八方散射的。于直线传播的假设，波实
50、际上是向四面八方散射的。于直线传播的假设，波实际上是向四面八方散射的。19由波散射引起的不均匀性由波散射引起的不均匀性由波散射引起的不均匀性由波散射引起的不均匀性 层析成像原则上可以用基于层析成像原则上可以用基于层析成像原则上可以用基于层析成像原则上可以用基于FourierFourier映射定理的算法实现映射定理的算法实现映射定理的算法实现映射定理的算法实现 For situations when one must take diffraction effects For situations when one must take diffraction effects(inhomogenei
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