[Rtk-users] Iterative reconstruction

[Simon Rit]

Hi,
This looks good to me, I haven't spotted anything completely wrong. Note
that without regularization, this is known to diverge after some iterations
because it starts to fit the noise.
I think SARTConeBeamReconstructionFilter will do something similar if you
set NumberOfProjectionsPerSubset
<http://www.openrtk.org/Doxygen/classrtk_1_1SARTConeBeamReconstructionFilter.html#a54db8838b0956a00df262f3595f4f7ef>
to the number of projections in your stack but it includes an additional
normalization term to account for the raylength. Since you don't have that,
I think you need a very small alpha. But 1e-5 should be small enough so
maybe you can check against it to see if the algorithms go in the same
direction.
The code is available online but we don't have any implementation details
to provide. CG is quite hard to grasp but SART should be easy enough to
follow.
Simon

On Wed, Sep 2, 2020 at 4:03 AM Zhang, Zhehao <zhehao.zhang at wustl.edu> wrote:

>
>
> Hi all,
>
>
>
> I have used RTK for a while, first of all, thanks for providing this great
> software.
>
>
>
> I am trying to perform some iterative CBCT reconstruction with a
> specifically defined regularization term recently. Since this
> regularization is not TV nor wavelet, I may not be able to directly use
> those RTK provided filters, like
> ‘ConjugateGradientConeBeamReconstructionFilter’. What I want is simply use
> gradient descent method and calculate the gradient of (1/2) ||(Rf - P)||^2
> and my regularization term. I got some problems on how to get the gradient
> of  (1/2) ||(Rf - P)||^2 , which should be R*(Rf - p), f is the required
> results, p is measured projections and R is forward projections. Hope to
> get some hints for you.
>
>
>
> Fow now, I tried to directly use  ‘JosephForwardProjectionImageFilter’
> and ‘JosephBackProjectionImageFilter’ to achieve this goal, however, the
> acquired values seems to be really large after several iterations. I think
> I must made something wrong. Could you please give me some suggestions
> about this problem if I want to utilize RTF to get gradient? Or is there
> any implementation detail of CG/SIRT filters that we can access (I am not
> sure if it is public)? I put my current code here (
> https://drive.google.com/file/d/1GPuoYHk4ACe5VDnVwZlsIzK1OHrM2AdK/view?usp=sharing
> )
>
>
>
> Thank you very much and best regards.
>
>
>
> Zhehao
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