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Up until now, we have been mentioning image reconstruction in PET,
but have not described this process.
Image reconstruction in PET images is done mainly using two approaches:
filtered back projection, or iterative reconstruction techniques.
Filtered back projection has been used historically due to its simplicity and speed,
while iterative reconstruction results in an estimate of
the true image, and requires more computer power to run in an efficient manner.
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This slide shows schematically the filtered back projection image reconstruction process.
Assume we have a point source in the center of the scanner.
The scan profiles (projections) of this point source from different angles are shown in figure A of the slide.
Back projecting these profiles along the image grid will result in figure B on the slide.
Notice that the image in B roughly represents the original object in figure A,
except for the additional spokes shown on the figure.
By filtering the projections (either before or after the back projection process),
while increasing the number of projections collected
the appearance of the object in the center of the image will be
enhanced, while that of the spokes will be suppressed.
Since this process requires back projection and filtering,
the overall process is known as 'filtered back projection'.
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Iterative reconstruction approaches the image reconstruction process in a different way.
One first 'guesses' an image, and then generates
the sinogram corresponding to the guessed image, via forward projection.
This will result in a guessed sinogram.
The measured sinogram will then be compared to the guessed sinogram.
If the ratio on a pixel-by-pixel basis is equal to unity,
the guessed image is the true representation of the acquired data.
If not, then the ratio of sinograms is back projected and modified to generate
an updated guess, which subsequently is forward projected to generate another guessed sinogram,
which in turn will be compared to the measured sinogram.
This process is iterated multiple times until a pre-set number of iterations
is achieved, or a pre-set tolerance error in the ratio sinogram is encountered.
The resulting guessed image will then correspond to the object being imaged.
In this regard, we can see that iterative reconstruction generates an estimate of the true image.
Since this process is performed on all the acquired sinograms simultaneously,
it will require extensive computational resources.
This fortunately, can easily be accomplished, using current high-performance computers.
This slide shows a comparison between
