MATLAB实现的医学图像FBP算法知识分享.ppt

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,The Filtered Backprojection Algorithm in MATLAB,Greg Gallardo,51:185,Filtered Backprojection Algorithm,Measure the family of projections,K,=#of projections(angles),N,=#of rays(detector size),Perform FFT ,Multiply FFT by FFT .,Perform IFFT product from step 3,Perform backprojection as:,1)Measure the family of projections,R,Xp=RADON(.)returns two variables,Matrix R columns are the Radon transform for the angles.Rows are detector position,Vector Xp-containing the radial coordinates corresponding to each row of R.,1)Measure the family of projections,Function parameters,size():gets N and K,nextpow2():get width for FFT,2)Perform FFT ,MATLAB,stands for,MAT,rix,LAB,oratory,Matrix operations are faster than visiting each element in a loop.,3)Multiply FFT by FFT ,Backprojection filters,Shepp-Logan:Ram-Lak multiplied by sinc function(see iradon help),Cosine:Ram-Lak multiplied by cosine,Hamming:Ram-Lak multiplied by Hamming window,Hanning,Blackman,etc.,3)Multiply FFT by FFT ,Ram-Lak,Shepp-Logan and Cosine filters in frequency domain,3)Multiply FFT by FFT ,FIR Filters.Commonly used Windows,Figure from“Discrete-Time Signal Processing”,Oppenheim&Schafer,Prentice-Hall,3)Multiply FFT by FFT ,Rectangular,Bartlett(triangular),Hanning(von Hann),Hamming,Blackman,from“Discrete-Time Signal Processing”,Oppenheim&Schafer,Prentice-Hall,3)Multiply FFT by FFT ,3)Multiply FFT by FFT ,3)Multiply FFT by FFT ,Filter step.Element by element multiplication,4)IFFTproduct from step 3,5)Perform Backprojection as:,Results,Results,