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Re: Radon forward projection problem [message #60070 is a reply to message #59981] Thu, 24 April 2008 09:22 Go to previous messageGo to previous message
mmiller3 is currently offline  mmiller3
Messages: 81
Registered: January 2002
Member
>>>> > "Wox" == Wox <nomail@hotmail.com> writes:

> Now what is OSEM doing?

OSEM uses a different subset of the data for each iteration. For
example, if you were running with 8 subsets, you'd use data from
angles 0, 7, 15, ... for the first iteration, the data from
angles 1, 8, 16, ... for the second iteration, 2, 9, 17, ... for
the third and so on in order - hence the name ordered subsets EM.
Each subset is handled using regular EM. Note that each subset
must be a reasonably complete measurement by itself. If too many
subset are used, the signal-to-noise in each subset will approach
zero and the method won't do any thing useful.

OSEM has the advantage of making each iteration take less time
then using the full data set each time, so it is computationally
feasible compared to EM. I noted that in your original posting,
you were asking about interpolating your sinograms before back
projecting. If you interpolate subsets to fill in larger
sinograms, you will loose some of the speed advantages of OSEM.

When run to "convergence," the OSEM result will sort of oscillate
between the subsets. Usually OSEM is stopped before that
happens, but the stopping point has to be determined empirically
- typically when the images look "good." Since the algorithm
hasn't fully converged at that point, there are issues with using
OSEM images for quantitative work. The same issues arise with
EM, since it will converge on the data, including the noise.
Since OSEM uses subsets, it will not even converge on the same
result as EM, if both where run to convergence.

In the medical world, OSEM is very commonly used for diagnostic
work, though. OSEM takes longer than filtered back projection,
but produces nicer/smoother images far more quickly than
quantitatively accurate methods such as MAP.

Mike

P.S. Note the use of 0-based indices for choosing angles - still
trying to stay on topic for IDL ;-)

--
Michael A. Miller mmiller3@iupui.edu
Imaging Sciences, Department of Radiology, IU School of Medicine

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