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Images reconstruction. Radon transform
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Starring effect and residual signal (bleeding out)
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Esempio : densità di spin “puntiforme”
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Back projected image R(x,y)
i = different angles
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Projection or central slice theorem
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To remove bleeding out and star effect : filtered back-projection
Example : M-filter, see text
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Limited to 1D but easily generalized to 2D and 3D
Continuous case Real obtained density
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Before going ahead some properties of FT
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If there’s a linear shift in k-space it can be demonstrasted that :
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Sampling function
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Relevant FT pairs for next discussion
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Discrete FT
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The final expression :
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Finally :
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