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Bleeding Out and Star Effect Reconstruction Using Radon Transform

Learn about the Radon transform, back-projected images, filtering techniques, and removing artifacts like bleeding out and star effects. Understand the properties of Fourier Transform and relevant FT pairs for signal reconstruction. Delve into 1D, 2D, and 3D imaging concepts and applications.

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Bleeding Out and Star Effect Reconstruction Using 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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