[Rtk-users] Result from SART is worse than from FDK

[Staude, Andreas]

Hi Simon,

I believe it really is a problem with the sum of the weights.

I first tried with the Shepp-Logan-phantom and afterwards with my data. 
The geometry is that of a standard cone-beam micro-CT.

The data I posted before were the reconstruction of just the middle 
plane. As I did the same with the Shepp-Logan-phantom data, similar 
effects were seen. As soon as one reconstructs a larger region around 
the middle plane, the artefacts vanish in the inner parts of the 
reconstructed volume, while in the top and bottom parts artefacts remain.

The program calls were:

create geometry:
----------------
rtksimulatedgeometry --nproj="1200" --output="geometry.xml" 
--sdd="1169.59" --sid="451.645" --arc="-360" --first_angle="360"

project the phantom:
--------------------
rtkprojectgeometricphantom -g geometry.xml -o projections3.mha --spacing 
2.5 --dimension 256 --phantomfile SheppLogan.txt

do a reference FDK reconstruction:
----------------------------------
rtkfdk -p . -r projections3.mha -o shepp-logan_fdk3_3D.mha -g 
geometry.xml --spacing 1 --dimension 256

SART reconstruction of middle plane:
------------------------------------
rtksart -p . -r projections3.mha -o shepp-logan_sart3_2D.mha -g 
geometry.xml --spacing 1 --dimension 256,1,256

SART reconstruction of 10 planes around middle plane:
-------------------------------------------------------
rtksart -p . -r projections3.mha -o shepp-logan_sart3_2.5D.mha -g 
geometry.xml --spacing 1 --dimension 256,10,256

SART reconstruction of whole object:
------------------------------------
rtksart -p . -r projections3.mha -o shepp-logan_sart3_3D.mha -g 
geometry.xml --spacing 1 --dimension 256


Reconstruction of more slices of the real data-set also gave a good 
result. Only the slices near bottom and top are not reconstructed correctly.

So it seems that the normalisation does not only take the values inside 
the reconstructed volume into account, but also (wrong) values outside.

What do you think?

Cheers,

Andreas



On 11/05/2013 07:11 PM, Simon Rit wrote:
> Hi Andreas,
> Thanks for the report. We know that the implementation of SART is
> imperfect, we haven't been working a lot on it... It seems that you
> haven't reached convergence. One potential cause is that we use a
> heuristic for the sum of the weights (denominator in the SART formula)
> instead of the exact sum. The weight is constant and equals the
> diagonal of your volume (see line 165 in
> rtkSARTConeBeamReconstructionFilter.txx). Maybe this is completely
> wrong in your case. Could you try to increase lambda to see if that
> helps?
> To help us do some tests, I would advise you do reproduce your
> geometry with simulations of the Shepp Logan phantom (see
> wiki.openrtk.org).
> Simon
>
> On Tue, Nov 5, 2013 at 5:11 PM, Staude, Andreas <andreas.staude at bam.de> wrote:
>> Hello RTk-users,
>>
>> I try to use the SART algorithm, but the results are worse than those
>> obtained with FDK (see attached images).
>>
>> The FDK result looks like expected, so I assume that I have the data
>> format and the reconstruction geometry set properly. For SART I used the
>> same parameters and already tried with different values of lambda and
>> niterations.
>>
>> Does anyone have an idea what went wrong? Is there some kind of
>> smoothing or regularisation applied in the SART implementation?
>>
>> Many thanks in advance!
>>
>> Cheers,
>>
>> Andreas
>>
>>
>> --
>>
>> ===============================================================
>> Dr. Andreas Staude
>> Fachbereich 8.5 "Mikro-ZfP", Computertomographie
>> BAM Bundesanstalt für Materialforschung und -prüfung
>> Unter den Eichen 87
>> D-12205 Berlin
>> Germany
>>
>> Tel.: ++49 30 8104 4140
>> Fax:  ++49 30 8104 1837
>> ===============================================================
>>
>>
>>
>>
>> _______________________________________________
>> Rtk-users mailing list
>> Rtk-users at openrtk.org
>> http://public.kitware.com/cgi-bin/mailman/listinfo/rtk-users
>>

-- 

===============================================================
Dr. Andreas Staude
Fachbereich 8.5 "Mikro-ZfP", Computertomographie
BAM Bundesanstalt für Materialforschung und -prüfung
Unter den Eichen 87
D-12205 Berlin
Germany

Tel.: ++49 30 8104 4140
Fax:  ++49 30 8104 1837
===============================================================