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Exact interior reconstruction with cone-beam CT.

Ye Y, Yu H, Wang G - Int J Biomed Imaging (2007)

Bottom Line: Our derivations are based on the so-called generalized PI-segment (chord).The available projection onto convex set (POCS) algorithm and singular value decomposition (SVD) method can be applied to perform the exact interior reconstruction.These results have many implications in the CT field and can be extended to other tomographic modalities, such as SPECT/PET, MRI.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA.

ABSTRACT
Using the backprojection filtration (BPF) and filtered backprojection (FBP) approaches, respectively, we prove that with cone-beam CT the interior problem can be exactly solved by analytic continuation. The prior knowledge we assume is that a volume of interest (VOI) in an object to be reconstructed is known in a subregion of the VOI. Our derivations are based on the so-called generalized PI-segment (chord). The available projection onto convex set (POCS) algorithm and singular value decomposition (SVD) method can be applied to perform the exact interior reconstruction. These results have many implications in the CT field and can be extended to other tomographic modalities, such as SPECT/PET, MRI.

No MeSH data available.


Variable change from  to .
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fig3: Variable change from to .

Mentions: For a fixed ,the filtering plane remains unchanged for all .As shown in Figure 3, we can change the variable to so that the direction for now points to the direction ,and the filtering direction is still specified clockwise. Let denote the angle from () to .Then, (6) can be rewritten as (7)f(r)=−12π2∫sbstds/r−ρ(s)/PV ×∫−ππ∂∂qDf(ρ(q),Θ(s,γ˜))/q=sdγ˜sin⁡(γ˜−θ(r,s)). Note that now is changed to which is independent of ,and the value of is negative.Our condition (i) implies that (8)PV∫θ(a,s)θ(c,s)∂∂qDf(ρ(q),Θ(s,γ˜))/q=sdγ˜sin⁡(γ˜−θ(r,s)) is known forany and for any on the line-segment .


Exact interior reconstruction with cone-beam CT.

Ye Y, Yu H, Wang G - Int J Biomed Imaging (2007)

Variable change from  to .
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2235933&req=5

fig3: Variable change from to .
Mentions: For a fixed ,the filtering plane remains unchanged for all .As shown in Figure 3, we can change the variable to so that the direction for now points to the direction ,and the filtering direction is still specified clockwise. Let denote the angle from () to .Then, (6) can be rewritten as (7)f(r)=−12π2∫sbstds/r−ρ(s)/PV ×∫−ππ∂∂qDf(ρ(q),Θ(s,γ˜))/q=sdγ˜sin⁡(γ˜−θ(r,s)). Note that now is changed to which is independent of ,and the value of is negative.Our condition (i) implies that (8)PV∫θ(a,s)θ(c,s)∂∂qDf(ρ(q),Θ(s,γ˜))/q=sdγ˜sin⁡(γ˜−θ(r,s)) is known forany and for any on the line-segment .

Bottom Line: Our derivations are based on the so-called generalized PI-segment (chord).The available projection onto convex set (POCS) algorithm and singular value decomposition (SVD) method can be applied to perform the exact interior reconstruction.These results have many implications in the CT field and can be extended to other tomographic modalities, such as SPECT/PET, MRI.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA.

ABSTRACT
Using the backprojection filtration (BPF) and filtered backprojection (FBP) approaches, respectively, we prove that with cone-beam CT the interior problem can be exactly solved by analytic continuation. The prior knowledge we assume is that a volume of interest (VOI) in an object to be reconstructed is known in a subregion of the VOI. Our derivations are based on the so-called generalized PI-segment (chord). The available projection onto convex set (POCS) algorithm and singular value decomposition (SVD) method can be applied to perform the exact interior reconstruction. These results have many implications in the CT field and can be extended to other tomographic modalities, such as SPECT/PET, MRI.

No MeSH data available.