[Rtk-users] Reconstructing from fan-beam projections

Tue May 16 13:22:00 EDT 2017

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.rit at gmail.com <simon.rit at gmail.com> på vegne af Simon Rit <simon.rit at creatis.insa-lyon.fr>
Sendt: 16. maj 2017 16:59:12
Til: Jacob Frøsig
Cc: rtk-users at 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 <jafs at force.dk<mailto:jafs at 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.rit at gmail.com<mailto:simon.rit at gmail.com> [mailto:simon.rit at gmail.com<mailto:simon.rit at gmail.com>] On Behalf Of Simon Rit
Sent: 16. maj 2017 14:54
To: Jacob Frøsig <jafs at force.dk<mailto:jafs at force.dk>>
Cc: rtk-users at openrtk.org<mailto:rtk-users at 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 <jafs at force.dk<mailto:jafs at 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-bounces at public.kitware.com<mailto:rtk-users-bounces at public.kitware.com>] On Behalf Of Simon Rit
Sent: 15. maj 2017 17:32
To: rtk-users at openrtk.org<mailto:rtk-users at 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 <jafs at force.dk<mailto:jafs at 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.rit at gmail.com<mailto:simon.rit at gmail.com> [mailto:simon.rit at gmail.com<mailto:simon.rit at gmail.com>] On Behalf Of Simon Rit
Sent: 15. maj 2017 16:05
To: louie L <ghostcz at hotmail.com<mailto:ghostcz at hotmail.com>>
Cc: Jacob Frøsig <jafs at force.dk<mailto:jafs at force.dk>>; rtk-users at public.kitware.com<mailto:rtk-users at 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 <ghostcz at hotmail.com<mailto:ghostcz at 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 <jafs at force.dk<mailto:jafs at 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

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