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Images reconstruction. Radon transform

Images reconstruction. Radon transform. Starring effect and residual signal (bleeding out). Esempio : densità di spin “puntiforme”. Back projected image R(x,y).  i = different angles. Projection or central slice theorem. To remove bleeding out and star effect : filtered back-projection

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Images reconstruction. Radon transform

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  1. Images reconstruction. Radon transform

  2. Starring effect and residual signal (bleeding out)

  3. Esempio : densità di spin “puntiforme”

  4. Back projected image R(x,y) i = different angles

  5. Projection or central slice theorem

  6. To remove bleeding out and star effect : filtered back-projection Example : M-filter, see text

  7. Limited to 1D but easily generalized to 2D and 3D Continuous case Real obtained density

  8. Before going ahead some properties of FT

  9. If there’s a linear shift in k-space it can be demonstrasted that :

  10. Sampling function

  11. Relevant FT pairs for next discussion

  12. Discrete FT

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