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COMPUTED TOMOGRAPHY IMAGE RECONSTRUCTION  Presented By: Gunjan Patel (MS-Medical Software ) (B.E.-Biomedical Engg.) (PGQ-Q...
History of Image Reconstruction <ul><li>1917 Radon  has developed mathematical solution to the  problems of image reconstr...
CT Image Reconstruction <ul><li>For an N×N image, we have N  unknowns to estimate the digital image reconstruction. </li><...
IMAGE RECONSTRUCTION
BACK PROJECTION METHOD <ul><li>The oldest method </li></ul><ul><li>Not used in commercial ct scanners </li></ul><ul><li>Me...
BACK PROJECTION METHOD <ul><li>Start from a projection value and back-project a ray of equal pixel values that would sum t...
Example:
Problem: <ul><li>Problems with back-projection include mainly severe blurring in the computed images </li></ul>
Iterative  reconstruction <ul><li>Successive approximation method  </li></ul><ul><li>Iterative least squares techniques </...
Example:  <ul><li>Successive approximation method to obtain an  image of attenuation coefficients  from the  measured inte...
 
Analytical methods <ul><li>Current Commercial scanner uses  this method </li></ul><ul><li>A mathematical technique known a...
1. Filtered  back projection (-) (-) (-) (+) (+) (+) Spatial Filter
1. Filtered  back projection <ul><li>This technique  elimination the unwanted cusp  like tails of the projection. </li></u...
1. Filtered  back projection f(x,y) f(x,y) P(  t) P’(  t)
2. Fourier filtering <ul><li>A property of the Fourier transform </li></ul><ul><li>Relates the projection data in the spat...
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 <ul><li>2D Fourier transformation: </li></ul><ul><li>The slice of the 2D Fourier transform at  k...
From Projections to Image y x Ky Kx F -1 [F(Kx,ky)] f(x,y) P(  t) F(Kx,Ky)
Reconstruction of  Object <ul><li>Interpolation can be used in the frequency domain to re-grid the radial sampling to unif...
References <ul><li>http://www.slideshare.net/NYCCT1199/ct-reconstruction-methods </li></ul><ul><li>http://en.wikipedia.org...
Queries !!!
 
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CT Scan Image reconstruction

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  • Hi All, We are planning to start Hadoop online training batch on this week... If any one interested to attend the demo please register in our website... For this batch we are also provide everyday recorded sessions with Materials. For more information feel free to contact us : siva@keylabstraining.com. For Course Content and Recorded Demo Click Here : http://www.keylabstraining.com/hadoop-online-training-hyderabad-bangalore
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  • These slides have serious problems. Slide 9 is plain wrong about sinograms. They have nothing to do with contrast agent. Also backprojection is a step of both iterative and analytical algorithms not an algorithm itself.
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CT Scan Image reconstruction

  1. 1. COMPUTED TOMOGRAPHY IMAGE RECONSTRUCTION Presented By: Gunjan Patel (MS-Medical Software ) (B.E.-Biomedical Engg.) (PGQ-Quality Management)
  2. 2. History of Image Reconstruction <ul><li>1917 Radon has developed mathematical solution to the problems of image reconstruction from of a set of projection . </li></ul><ul><li>Utilization in solving problems in astronomy and optics. </li></ul><ul><li>1961 finally these techniques were used in medical field . </li></ul>
  3. 3. CT Image Reconstruction <ul><li>For an N×N image, we have N unknowns to estimate the digital image reconstruction. </li></ul>2 pixel
  4. 4. IMAGE RECONSTRUCTION
  5. 5. BACK PROJECTION METHOD <ul><li>The oldest method </li></ul><ul><li>Not used in commercial ct scanners </li></ul><ul><li>Method is analogous to a graphic reconstruction </li></ul><ul><li>Processing part is simple and direct </li></ul><ul><li>Each projection can not contribute originally formal of profile </li></ul><ul><li>Some produces images are ‘Starred’ and ‘blurring’ that makes unsuitable for medical diagnosis </li></ul><ul><li>A sinogram is a special x-ray procedure that is done with contrast media (x-ray dye) to visualize any abnormal opening (sinus) in the body </li></ul>
  6. 6. BACK PROJECTION METHOD <ul><li>Start from a projection value and back-project a ray of equal pixel values that would sum to the same value </li></ul><ul><li>Back-projected ray is added to the estimated image and the process is repeated for all projection points at all angles </li></ul><ul><li>With sufficient projection angles, structures can be somewhat restored </li></ul>
  7. 7. Example:
  8. 8. Problem: <ul><li>Problems with back-projection include mainly severe blurring in the computed images </li></ul>
  9. 9. Iterative reconstruction <ul><li>Successive approximation method </li></ul><ul><li>Iterative least squares techniques </li></ul><ul><li>Algebraic reconstruction </li></ul><ul><ul><li>Hounsfield used this technique in his </li></ul></ul><ul><ul><li>First EMI BRAIN SCANNER </li></ul></ul><ul><li>Iterative methods are not use in today commercial scanners </li></ul>
  10. 10. Example: <ul><li>Successive approximation method to obtain an image of attenuation coefficients from the measured intensity form Object slice </li></ul><ul><li>The attenuation coefficient of the object are unknown before hand </li></ul><ul><ul><li>Calculation of Method: Click </li></ul></ul>
  11. 12. Analytical methods <ul><li>Current Commercial scanner uses this method </li></ul><ul><li>A mathematical technique known as convolution or filtering </li></ul><ul><li>Technique employs a spatial filter for remove blurring artifacts. </li></ul><ul><li>2 types of method </li></ul><ul><ul><li>Filtered back projection </li></ul></ul><ul><ul><li>Fourier filtering </li></ul></ul>
  12. 13. 1. Filtered back projection (-) (-) (-) (+) (+) (+) Spatial Filter
  13. 14. 1. Filtered back projection <ul><li>This technique elimination the unwanted cusp like tails of the projection. </li></ul><ul><li>The projection data are convoluted with suitable processing function before back projection </li></ul><ul><li>The filter function has negative side lobes surrounding a positive core , so that in summing the filtered back projection - positive and negative contribution that cancel outside the central core  The constructed image resemble Original object </li></ul>
  14. 15. 1. Filtered back projection f(x,y) f(x,y) P(  t) P’(  t)
  15. 16. 2. Fourier filtering <ul><li>A property of the Fourier transform </li></ul><ul><li>Relates the projection data in the spatial domain to the Frequency domain </li></ul>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
  16. 17. Fourier Transform to Projection
  17. 18. Fourier Slice Theorem Ky Kx  F(Kx,Ky) F[P(  t)] P(  t) f(x,y) t  y x X-rays
  18. 19. Mathematical Illustration <ul><li>2D Fourier transformation: </li></ul><ul><li>The slice of the 2D Fourier transform at kx=0 is given by: </li></ul><ul><li>and at ky=0 is given by </li></ul>
  19. 20. From Projections to Image y x Ky Kx F -1 [F(Kx,ky)] f(x,y) P(  t) F(Kx,Ky)
  20. 21. Reconstruction of Object <ul><li>Interpolation can be used in the frequency domain to re-grid the radial sampling to uniform sampling </li></ul><ul><li>Inverse DFT can then be efficiently used to compute the object </li></ul>Freq. domain Interpolation IDFT Computed Object
  21. 22. References <ul><li>http://www.slideshare.net/NYCCT1199/ct-reconstruction-methods </li></ul><ul><li>http://en.wikipedia.org/wiki/Iterative_reconstruction </li></ul><ul><li>Handbook of Biomedical Instrumentation-R.S.Khandpur </li></ul>
  22. 23. Queries !!!

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