[Rtk-users] Reconstructing from fan-beam projections

[Simon Rit]

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> 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] *On Behalf Of *Simon
> Rit
> *Sent:* 16. maj 2017 14:54
> *To:* Jacob Frøsig <jafs at force.dk>
> *Cc:* 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> 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] *On
> Behalf Of *Simon Rit
> *Sent:* 15. maj 2017 17:32
> *To:* 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> 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] *On Behalf Of *Simon
> Rit
> *Sent:* 15. maj 2017 16:05
> *To:* louie L <ghostcz at hotmail.com>
> *Cc:* Jacob Frøsig <jafs at force.dk>; 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> 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>:
>
> 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
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>
> Phone: +45 43 25 00 00 <+45%2043%2025%2000%2000>
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