CT Scan Image reconstruction

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  • 1. COMPUTED TOMOGRAPHY IMAGE RECONSTRUCTION Presented By: Gunjan Patel (MS-Medical Software ) (B.E.-Biomedical Engg.) (PGQ-Quality Management)
  • 2. History of Image Reconstruction
    • 1917 Radon has developed mathematical solution to the problems of image reconstruction from of a set of projection .
    • Utilization in solving problems in astronomy and optics.
    • 1961 finally these techniques were used in medical field .
  • 3. CT Image Reconstruction
    • For an N×N image, we have N unknowns to estimate the digital image reconstruction.
    2 pixel
  • 4. IMAGE RECONSTRUCTION
  • 5. BACK PROJECTION METHOD
    • The oldest method
    • Not used in commercial ct scanners
    • Method is analogous to a graphic reconstruction
    • Processing part is simple and direct
    • Each projection can not contribute originally formal of profile
    • Some produces images are ‘Starred’ and ‘blurring’ that makes unsuitable for medical diagnosis
    • 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
  • 6. BACK PROJECTION METHOD
    • Start from a projection value and back-project a ray of equal pixel values that would sum to the same value
    • Back-projected ray is added to the estimated image and the process is repeated for all projection points at all angles
    • With sufficient projection angles, structures can be somewhat restored
  • 7. Example:
  • 8. Problem:
    • Problems with back-projection include mainly severe blurring in the computed images
  • 9. Iterative reconstruction
    • Successive approximation method
    • Iterative least squares techniques
    • Algebraic reconstruction
      • Hounsfield used this technique in his
      • First EMI BRAIN SCANNER
    • Iterative methods are not use in today commercial scanners
  • 10. Example:
    • Successive approximation method to obtain an image of attenuation coefficients from the measured intensity form Object slice
    • The attenuation coefficient of the object are unknown before hand
      • Calculation of Method: Click
  • 11.  
  • 12. Analytical methods
    • Current Commercial scanner uses this method
    • A mathematical technique known as convolution or filtering
    • Technique employs a spatial filter for remove blurring artifacts.
    • 2 types of method
      • Filtered back projection
      • Fourier filtering
  • 13. 1. Filtered back projection (-) (-) (-) (+) (+) (+) Spatial Filter
  • 14. 1. Filtered back projection
    • This technique elimination the unwanted cusp like tails of the projection.
    • The projection data are convoluted with suitable processing function before back projection
    • 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
  • 15. 1. Filtered back projection f(x,y) f(x,y) P(  t) P’(  t)
  • 16. 2. Fourier filtering
    • A property of the Fourier transform
    • Relates the projection data in the spatial domain to the Frequency domain
    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
  • 17. Fourier Transform to Projection
  • 18. Fourier Slice Theorem Ky Kx  F(Kx,Ky) F[P(  t)] P(  t) f(x,y) t  y x X-rays
  • 19. Mathematical Illustration
    • 2D Fourier transformation:
    • The slice of the 2D Fourier transform at kx=0 is given by:
    • and at ky=0 is given by
  • 20. From Projections to Image y x Ky Kx F -1 [F(Kx,ky)] f(x,y) P(  t) F(Kx,Ky)
  • 21. Reconstruction of Object
    • Interpolation can be used in the frequency domain to re-grid the radial sampling to uniform sampling
    • Inverse DFT can then be efficiently used to compute the object
    Freq. domain Interpolation IDFT Computed Object
  • 22. References
    • http://www.slideshare.net/NYCCT1199/ct-reconstruction-methods
    • http://en.wikipedia.org/wiki/Iterative_reconstruction
    • Handbook of Biomedical Instrumentation-R.S.Khandpur
  • 23. Queries !!!
  • 24.