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10 Backprojection usually produce a blurred version of the image.

BP: Numerical Example

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2D-FT(I) 1D-FT(Radon(I)) 0°10° 90° 120° 17

18 Fundamentals of Medical Imaging Paul Suentes

19 2D Inverse Fourier Transform Function we want to reconstruct Let’s change F from cartesian coordinates to polar coordinates

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21 Form half lines to full lines :

22 Now the Central Slice Theorem become simply : And therefore:

23 And its 1D inverse Fourier transform from k to r. In the Radon domain it’s a convolution over r :

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25 Note that it’s a backprojection ! This is called Filtered Backprojection

26 Fundamentals of Medical Imaging Paul Suentes

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31 Ram-Lak Filter (or smoothed version of it) Projections Backproject Reconstructed image

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Rectification

Rectification

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