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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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Transcript of "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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