医学影像物理学课件：06yj-X-ray CT01

1、X-ray Computed Tomography,X-ray CT (Computed Tomography) is a kind of technique for making detailed X-rays of a cross section of a solid object. It is a great achievement in medical imaging technology after discover of X-ray. Two inventors of X-ray CT, GNHousfield and AMCormack got the Nobel Prize o

2、f physiology and medicine in 1979.,Disadvantage of traditional Photography,A disadvantage of X-ray photographs of the body is that they provide only an integrated value of the attenuation coefficient.,Primitive Tomography,Both X-ray source and the film are moved along axis of body, but their directi

3、on are opposite each other. The ratio of distance from point a to X-ray source to that of a to film is just equal to the ratio of their moving speed. Hence the X-rays passing through point A in the plane always strike the same points on the film. X-ray passing through points out of the plane strike

4、many points on the film, and structure there is blurred out.,Transverse Scan,Scan plane is a transverse plane A beam of X-rays Move in synchrony Clear cross section image,Basic Concept,断层/Section/解剖断面 Pixel Voxel,The Nature of CT: The Array of,扫描/Scanning,1 Acquire MonoChromic X-ray 2 Acquire Narrow

5、 X-ray Beam,Lead collimator,扫描方式,Scan Device,X-ray tube Collimator Scan bed Detector array Data Collection circuit,Projection 投影与投影函数: 投射到受检体后X射线的出射强度称为投影值. 投影值的分布成为投影函数.,从投影数据到图像的重建,受检体扫描 从不同的路径获得足够投影值 数学处理 获得吸收系数的二维分布 形成图像,此处的衰减系数为平均衰减系数.,Concept of Projection,I0,In,Spatial Position of Path,Dirac

6、Function,奇异函数：单位斜坡函数、阶跃函数、单位冲激函数,定义式：,冲激函数的抽样特性：,2D Dirac Function,卷积/Convolution,具有相同自变量的两函数做如下运算：,离散序列,卷积特性,卷积的意义：一个函数不动，另一个函数移动时，两个函数重叠区域的面积,频域与时域:,卷积图解说明,变量置换 反褶 平移 相乘 积分 求面积,例:对均匀圆柱体投影的卷积处理,P68,System 系统,线性系统 时（移）不变系统,SYSTEM,激励,响应,f(x),g(x),F(x),G(x),a*f(x)+b*g(x),aF(x)+bG(x),f(t-a),F(t-a),PSF

7、(Point Spread Function),在一维线性系统中表征系统特性可用冲激响应函数h(t):,在二维线性系统中，将所得到的表征系统特性的响应定义为该系统的点扩展函数 h(t):,二维Dirac函数在成像系统中被称为点源或点质量。,成像系统的响应,Dirac函数的抽样性：,将f(x,y)施于点扩展函数为h(x,y)的线性移不变系统后得到响应,对于线性移不变系统，响应g(x,y)是输入函数f(x,y)与系统的点扩展函数h(x,y)的卷积。,理想系统,对于任一成像系统，若其点扩展函数为Dirac函数，即,称为理想系统。,输入点源，输出也是点源。,输入f(x,y)，输出:,如果 ，该系统为非理想系统，输入f(x,y)将不等于输出。输出裙边将会