Hi Vahid,
Welcome to RTK :)
Indeed, there are several iterative methods already implemented in RTK,
but none of the filters allows you to easily extract the gradient of the
least squares function there are minimizing.
If you need to minimize the classical non-regularized tomographic cost
function, ie || R f - p ||², with R the forward projection operator, f
the volume you are looking for, and p the measured projections, my best
advice would be to copy some part of the pipeline of
rtkSARTConeBeamReconstructionFilter to get the job done, ie the
following part (copy-paste this into webgraphviz.com)
digraph SARTConeBeamReconstructionFilter {
Input0 [ label="Input 0 (Volume)"];
Input0 [shape=Mdiamond];
Input1 [label="Input 1 (Projections)"];
Input1 [shape=Mdiamond];
node [shape=box];
ForwardProject [ label="rtk::ForwardProjectionImageFilter" URL="\ref
rtk::ForwardProjectionImageFilter"];
Extract [ label="itk::ExtractImageFilter" URL="\ref
itk::ExtractImageFilter"];
MultiplyByZero [ label="itk::MultiplyImageFilter (by zero)" URL="\ref
itk::MultiplyImageFilter"];
AfterExtract [label="", fixedsize="false", width=0, height=0, shape=none];
Subtract [ label="itk::SubtractImageFilter" URL="\ref
itk::SubtractImageFilter"];
MultiplyByLambda [ label="itk::MultiplyImageFilter (by lambda)"
URL="\ref itk::MultiplyImageFilter"];
Divide [ label="itk::DivideOrZeroOutImageFilter" URL="\ref
itk::DivideOrZeroOutImageFilter"];
GatingWeight [ label="itk::MultiplyImageFilter (by gating weight)"
URL="\ref itk::MultiplyImageFilter", style=dashed];
Displaced [ label="rtk::DisplacedDetectorImageFilter" URL="\ref
rtk::DisplacedDetectorImageFilter"];
ConstantProjectionStack [ label="rtk::ConstantImageSource" URL="\ref
rtk::ConstantImageSource"];
ExtractConstantProjection [ label="itk::ExtractImageFilter" URL="\ref
itk::ExtractImageFilter"];
RayBox [ label="rtk::RayBoxIntersectionImageFilter" URL="\ref
rtk::RayBoxIntersectionImageFilter"];
ConstantVolume [ label="rtk::ConstantImageSource" URL="\ref
rtk::ConstantImageSource"];
BackProjection [ label="rtk::BackProjectionImageFilter" URL="\ref
rtk::BackProjectionImageFilter"];
OutofInput0 [label="", fixedsize="false", width=0, height=0, shape=none];
OutofBP [label="", fixedsize="false", width=0, height=0, shape=none];
BeforeBP [label="", fixedsize="false", width=0, height=0, shape=none];
BeforeAdd [label="", fixedsize="false", width=0, height=0, shape=none];
Input0 -> OutofInput0 [arrowhead=none];
OutofInput0 -> ForwardProject;
ConstantVolume -> BeforeBP [arrowhead=none];
BeforeBP -> BackProjection;
Extract -> AfterExtract[arrowhead=none];
AfterExtract -> MultiplyByZero;
AfterExtract -> Subtract;
MultiplyByZero -> ForwardProject;
Input1 -> Extract;
ForwardProject -> Subtract;
Subtract -> MultiplyByLambda;
MultiplyByLambda -> Divide;
Divide -> GatingWeight;
GatingWeight -> Displaced;
ConstantProjectionStack -> ExtractConstantProjection;
ExtractConstantProjection -> RayBox;
RayBox -> Divide;
Displaced -> BackProjection;
BackProjection -> OutofBP [arrowhead=none];
}
As you can see, it is a very large part of the SART reconstruction
filter, so yoiu might be better off just copying the whole
SARTConeBeamReconstructionFilter and modifying it.
Of course, you could also look into ITK's cost function class, and see
if one of the classes inherited from it suits your needs, implement your
cost function this way, and use ITK's off-the-shelf solvers to minimize
it. See the inheritance diagram in
https://itk.org/Doxygen/html/classitk_1_1CostFunctionTemplate.html if
you want to try this approach.
Best regards,
Cyril
On 11/01/2016 05:50 PM, vahid ettehadi via Rtk-users wrote:
Hello RTK users and developers,
I already implemented the RTK and reconstructed some images with the
FDK algorithm implemented in RTK. It works well. Thanks to RTK developers.
Now, I am trying to develop a model-based image reconstruction for our
cone-beam micro-CT. I see already that some iterative algorithms like
ART and its modifications and conjugate-gradient (CG) method are
implemented in the RTK. I want to develop a model-based reconstruction
through the Newton/quasi-Newton optimizations methods. I was wondering
is it possible to extract the gradient of least square function from
implemented algorithms like CG module? Any recommendation will be
appreciated.
Best Regards,
Vahid
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