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# 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.