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Filtered Backprojection

The technique is comprised of two sequential steps: filtering projections followed by backprojecting the filtered projections. Though these two steps are sequential, each view position can be processed independently.

Parallel Computer Processing
Since each view can be processed independently, filtered backprojection is amendable to parallel processing. Indeed, this has been used in commercial scanners to speed reconstruction. This parallelism is exploited both in the CTSim graphical shell and in the LAM version of CTSimText. CTSim can distribute it's workload amongst multiple processors working in parallel.

The graphical shell will automatically take advantage of multiple CPU's when running on a Symmetric Multiprocessing computer. Dual-CPU computers are commonly available which provide a near doubling in reconstruction speeds. CTSim, though, has no limits on the number of CPU's that can be used in parallel. The LAM version of CTSimText is designed to work in a cluster of computers. This has been testing with a cluster of 16 computers in a Beowulf-class cluster with excellent results.

Filter projections
The first step in filtered backprojection reconstructions is the filtering of each projection. The projections for a each view have their frequency data multipled by a filter of |w|. CTSim permits four different ways to accomplish this filtering.

Two of the methods use convolution of the projection data with the inverse Fourier transform of |w|. The other two methods perform an Fourier transform of the projection data and multiply that by the |w| filter and then perform an inverse fourier transform.

Though multiplying by |w| gives the sharpest reconstructions, in practice, superior results are obtained by reducing the higher frequencies. This is performed by mutiplying the |w| filter by another filter that attenuates the higher frequencies. CTSim has multiple filters for this purpose.

Backprojection of filtered projections
Backprojection is the process of "smearing'' the filtered projections over the reconstructing image. Various levels of interpolation can be specified.