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| A new iterative algorithm is introduced for a kind of inverse problem.
An example of this kind of inverse problem is CT image reconstruction.
The solution of non-iteration algorithm differs from the original
object. The difference between the solution and original object is
the error which is comprised of artifacts and noise. Compared to non-iteration
algorithm, the refinement iterative inverse (RII) algorithm can reduce
the artifacts but it increases the noise in the same time. Hence in
general the quality of reconstructed image is not much improved. In
other hand, the new iterative algorithm can reduce artifacts similar
to the RII algorithm; however it does not increase the noise. Hence
the image quality is improved a lot. The idea of the new iterative
algorithm came from an iterative reconstruction and re-projection
algorithm used in image reconstruction with limited field of view~(LFOV).
This algorithm led to the iterative reconstruction in sub-regions
(IRSR) in case the field of view(FOV) is unlimited. The sub-regions
are square boxes. In this case there were cracks (or grid) between
sub-regions. In order to eliminate the cracks, margins between sub-regions
were introduced. Taking the sub-regions as small as only one pixel
and keeping the margins led to the new iterative algorithm in this
paper. It is referred as iterative inverse in local-regions (IILR).
The error transfer function, artifact transfer function and filtering
function are compared between the IILR algorithm and the RII algorithm.
A simple example shows that the error obtained from the IILR algorithm
is smaller than that obtained from non-iteration algorithm in the
whole region, but the error obtained from the RII algorithm is smaller
than non-iteration algorithm only at the vicinity of the image edges.
It is proved that the RII algorithm is a special example of the IILR
algorithm when the margin is taken as zero.
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| Keywords:image reconstruction, inverse problem, back-projection |
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