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COMPUTED TOMOGRAPHY IMAGE RECONSTRUCTION  Presented By: Gunjan Patel (MS-Medical Software ) (B.E.-Biomedical Engg.) (PGQ-Quality Management)
History of Image Reconstruction ,[object Object],[object Object],[object Object]
CT Image Reconstruction ,[object Object],2 pixel
IMAGE RECONSTRUCTION
BACK PROJECTION METHOD ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
BACK PROJECTION METHOD ,[object Object],[object Object],[object Object]
Example:
Problem: ,[object Object]
Iterative  reconstruction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example:  ,[object Object],[object Object],[object Object]
 
Analytical methods ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
1. Filtered  back projection (-) (-) (-) (+) (+) (+) Spatial Filter
1. Filtered  back projection ,[object Object],[object Object],[object Object]
1. Filtered  back projection f(x,y) f(x,y) P(  t) P’(  t)
2. Fourier filtering ,[object Object],[object Object],The 1D Fourier transform of the projection of an image at an angle θ  The slice of the 2D Fourier transform at the same angle
Fourier Transform to Projection
Fourier Slice Theorem Ky Kx  F(Kx,Ky) F[P(  t)] P(  t) f(x,y) t  y x X-rays
Mathematical Illustration ,[object Object],[object Object],[object Object]
From Projections to Image y x Ky Kx F -1 [F(Kx,ky)] f(x,y) P(  t) F(Kx,Ky)
Reconstruction of  Object ,[object Object],[object Object],Freq. domain Interpolation IDFT Computed Object
References ,[object Object],[object Object],[object Object]
Queries !!!
 

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