Hi,

yes, it is indeed an interior- / region of interest problem in the sense that 
we only are interested in the fully illuminated centre region.
I have previously had success in getting good reconstructions from interior 
data using variational formulation with tailored penalty term. However, this is 
implemented in Matlab and the aim is to use your implementation to get a C++ 
implementation of this method.

But for now, I am just figuring how to do a simple reconstruction to get a 
grasp on the library.


Best regards,


Jacob




________________________________
Fra: simon....@gmail.com <simon....@gmail.com> på vegne af Simon Rit 
<simon....@creatis.insa-lyon.fr>
Sendt: 16. maj 2017 16:59:12
Til: Jacob Frøsig
Cc: rtk-us...@openrtk.org
Emne: Re: [Rtk-users] Reconstructing from fan-beam projections

Hi,
If this is true, then the sinogram indicates that you are dealing with an 
interior problem since you have high line integrals at the border (see enclosed 
profile). Is that indeed the case? If yes, that's a difficult problem...
Simon

On Tue, May 16, 2017 at 3:16 PM, Jacob Frøsig 
<j...@force.dk<mailto:j...@force.dk>> wrote:
Hi,

The attached sinogram consist of line integral values, i.e., sinogram(i,j) = 
-ln[ I(i,j)/I_0(i) ] where I and ­I_0 are the measured intensities with and 
without an object, respectively.
Since we are measuring with a line detector, the “zero” (I_0) is in this case 
just an array.
j is the index for the projections, i.e., j ∈  {1,2,…,360} since we take one 
projection for each whole angle.
I hope this explains the sinogram and again; thank you for your time!
Best regards,
Jacob

From: simon....@gmail.com<mailto:simon....@gmail.com> 
[mailto:simon....@gmail.com<mailto:simon....@gmail.com>] On Behalf Of Simon Rit
Sent: 16. maj 2017 14:54
To: Jacob Frøsig <j...@force.dk<mailto:j...@force.dk>>
Cc: rtk-us...@openrtk.org<mailto:rtk-us...@openrtk.org>

Subject: Re: [Rtk-users] Reconstructing from fan-beam projections

Hi Jacob,
Thanks for the image of the sinogram. I don't understand this sinogram. Do you 
know how to convert each pixel value to a line integral? I.e., if it's x-ray 
imaging, do you have an image without object?
Thanks,
Simon

On Tue, May 16, 2017 at 2:24 PM, Jacob Frøsig 
<j...@force.dk<mailto:j...@force.dk>> wrote:
Hi again,
and thank you for the example!
I have some trouble getting a proper reconstruction. If you have the time, any 
help would be appreciated.
Attached is my fan-beam sinogram as a .tif file. Here, projections are taken 
for 360 degrees and the detector has 507 pixels.
I believe the issue lies in setting the geometry and maybe the spacing between 
the pixels. The measurement geometry is as follows
Source to centre: 590 mm
Source to detector: 1000 mm
Detector length: 411mm

Best regards,

Jacob


From: Rtk-users 
[mailto:rtk-users-boun...@public.kitware.com<mailto:rtk-users-boun...@public.kitware.com>]
 On Behalf Of Simon Rit
Sent: 15. maj 2017 17:32
To: rtk-us...@openrtk.org<mailto:rtk-us...@openrtk.org>

Subject: Re: [Rtk-users] Reconstructing from fan-beam projections

Hi,
I have added an example here:
http://wiki.openrtk.org/index.php/FanBeam
The values in the first and the third rows are not used, as illustrated in this 
example. We add them to do a 2D interpolation but we do this 2D interpolation 
exactly on the second row so that's not a problem.
Note that it's a bit more tricky for iterative recon but we also have a 
solution for this if you need it.
Best regards,
Simon

On Mon, May 15, 2017 at 4:31 PM, Jacob Frøsig 
<j...@force.dk<mailto:j...@force.dk>> wrote:
Hi again,

Thank you for the quick answer! An example would be great, thanks. I have one 
concern about copying the fan-beam data:

Then we would have 2D projections for which each column is the same fan-beam 
projection. By this, values of the same row are equal even though the cone-beam 
geometry indicates the outer columns correspond to intensities of rays with  
longer travel time through the object and hence should have attenuated more. Is 
this neglectable?

Again, thanks!

Best regards,
Jacob



From: simon....@gmail.com<mailto:simon....@gmail.com> 
[mailto:simon....@gmail.com<mailto:simon....@gmail.com>] On Behalf Of Simon Rit
Sent: 15. maj 2017 16:05
To: louie L <ghos...@hotmail.com<mailto:ghos...@hotmail.com>>
Cc: Jacob Frøsig <j...@force.dk<mailto:j...@force.dk>>; 
rtk-users@public.kitware.com<mailto:rtk-users@public.kitware.com>
Subject: Re: [Rtk-users] Reconstructing from fan-beam projections

Hi,
I agree. What I do is do a 3 slice sinogram from the fan-beam projections by 
copying the same data in each slice but reconstruct one 2D slice. If you need 
an example, I can quickly demonstrate this in a short Python script.
Simon

On Mon, May 15, 2017 at 4:01 PM, louie L 
<ghos...@hotmail.com<mailto:ghos...@hotmail.com>> wrote:
Hi,

I think you can carefully pad zeros to your projections. Reconstruct as if it 
is a 3d object. Take the middle slice as your fanbeam result.
Let me know if it helps.

Best regards,
Louie

Sent from my iOS

Am 15.05.2017 um 15:55 schrieb Jacob Frøsig 
<j...@force.dk<mailto:j...@force.dk>>:
Dear Rtk-users

I was wandering if Rtk includes an implementation of a reconstruction method to 
reconstruct a 2D representation of an object given  fan-beam projections.
Or, if anyone has experience using e.g. FDKConeBeamReconstructionFilter  on 
projections from line-detectors (fan-beam instead of cone-beam).

I hope you guys can help.
Yours sincerely
Jacob Frøsig

Project Manager
Sensor Innovation

FORCE Technology
Park Allé 345
2605 Brøndby
Denmark

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