Andy Scacco

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Filtered Back Projection

• Andy Scacco
• John Smith

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Key Advantages

• Simple
• Effective
• Efficient
• Free Parameter
• Popular

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Theory
denotes a Radon Transform
g(s,T) Sinogram
f(x,y)
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Forward Projection
f
r
f
r
Sinogram
Image
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Back Projection Smearing
f
?
r
f
r
Image
Sinogram
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Real-Time Reconstruction Process
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Back Projection Result
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Tri-diagonal Toeplitz Filter Function


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Parameter ß Results
ß0
ß0.400
ß0.495
Original
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Timing
N
N
Radius
Angle
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All for naught

• FBP is implemented in MATLAB as

iradon(array,?T)
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Summary

• There exists an optimal, perhaps unique, ß
• Timing is very nearly N3
• MATLAB implementation is iradon(array,?T)