#include <rtkADMMWaveletsConeBeamReconstructionFilter.h>

Inheritance diagram for rtk::ADMMWaveletsConeBeamReconstructionFilter< TOutputImage >:

Collaboration diagram for rtk::ADMMWaveletsConeBeamReconstructionFilter< TOutputImage >:

Public Types
using	AddFilterType = itk::AddImageFilter< TOutputImage >

using	BackProjectionFilterType = rtk::BackProjectionImageFilter< TOutputImage, TOutputImage >

using	BackProjectionType = typename Superclass::BackProjectionType

using	CGOperatorFilterType = rtk::ADMMWaveletsConjugateGradientOperator< TOutputImage >

using	ConjugateGradientFilterType = rtk::ConjugateGradientImageFilter< TOutputImage >

using	DisplacedDetectorFilterType = rtk::DisplacedDetectorImageFilter< TOutputImage >

using	ForwardProjectionFilterType = rtk::ForwardProjectionImageFilter< TOutputImage, TOutputImage >

using	ForwardProjectionType = typename Superclass::ForwardProjectionType

using	MultiplyFilterType = itk::MultiplyImageFilter< TOutputImage >

using	Pointer = itk::SmartPointer< Self >

using	Self = ADMMWaveletsConeBeamReconstructionFilter

using	SoftThresholdFilterType = rtk::DeconstructSoftThresholdReconstructImageFilter< TOutputImage >

using	SubtractFilterType = itk::SubtractImageFilter< TOutputImage >

using	Superclass = IterativeConeBeamReconstructionFilter< TOutputImage, TOutputImage >

Public Types inherited from rtk::IterativeConeBeamReconstructionFilter< TOutputImage, TOutputImage >
using	BackProjectionFilterType = rtk::BackProjectionImageFilter< TOutputImage, VolumeType >

using	BackProjectionPointerType = typename BackProjectionFilterType::Pointer

enum	BackProjectionType

using	ConstPointer = itk::SmartPointer< const Self >

using	ForwardProjectionFilterType = rtk::ForwardProjectionImageFilter< VolumeType, TOutputImage >

using	ForwardProjectionPointerType = typename ForwardProjectionFilterType::Pointer

enum	ForwardProjectionType

using	Pointer = itk::SmartPointer< Self >

using	Self = IterativeConeBeamReconstructionFilter

using	Superclass = itk::ImageToImageFilter< TOutputImage, TOutputImage >

using	TClipImageType = itk::Image< double, VolumeType::ImageDimension >

using	VolumeType = TOutputImage

Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother () const

virtual float	GetAL_iterations ()

virtual float	GetAlpha ()

virtual float	GetBeta ()

virtual float	GetCG_iterations ()

virtual unsigned int	GetNumberOfLevels ()

virtual unsigned int	GetOrder ()

virtual void	SetAL_iterations (float _arg)

virtual void	SetAlpha (float _arg)

virtual void	SetBeta (float _arg)

virtual void	SetCG_iterations (float _arg)

virtual void	SetGeometry (ThreeDCircularProjectionGeometry *_arg)

virtual void	SetNumberOfLevels (unsigned int _arg)

virtual void	SetOrder (unsigned int _arg)


virtual const char *	GetNameOfClass () const


virtual void	SetDisableDisplacedDetectorFilter (bool _arg)

virtual bool	GetDisableDisplacedDetectorFilter ()

Public Member Functions inherited from rtk::IterativeConeBeamReconstructionFilter< TOutputImage, TOutputImage >
virtual ::itk::LightObject::Pointer	CreateAnother () const

virtual void	SetForwardProjectionFilter (ForwardProjectionType fwtype)

ForwardProjectionType	GetForwardProjectionFilter ()

virtual void	SetBackProjectionFilter (BackProjectionType bptype)

BackProjectionType	GetBackProjectionFilter ()

void	SetAttenuationMap (const VolumeType *attenuationMap)

VolumeType::ConstPointer	GetAttenuationMap ()

void	SetInferiorClipImage (const TClipImageType *inferiorClipImage)

TClipImageType::ConstPointer	GetInferiorClipImage ()

void	SetSuperiorClipImage (const TClipImageType *superiorClipImage)

TClipImageType::ConstPointer	GetSuperiorClipImage ()

virtual double	GetSigmaZero ()

virtual void	SetSigmaZero (double _arg)

virtual double	GetAlphaPSF ()

virtual void	SetAlphaPSF (double _arg)

virtual double	GetStepSize () const

virtual void	SetStepSize (double _arg)

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from rtk::IterativeConeBeamReconstructionFilter< TOutputImage, TOutputImage >
static Pointer	New ()

Protected Member Functions
	ADMMWaveletsConeBeamReconstructionFilter ()

void	GenerateData () override

void	VerifyInputInformation () const override

void	VerifyPreconditions () const override

	~ADMMWaveletsConeBeamReconstructionFilter () override=default


void	GenerateInputRequestedRegion () override

void	GenerateOutputInformation () override

Protected Member Functions inherited from rtk::IterativeConeBeamReconstructionFilter< TOutputImage, TOutputImage >
virtual BackProjectionPointerType	InstantiateBackProjectionFilter (int bptype)

BackProjectionPointerType	InstantiateCudaBackProjection ()

BackProjectionPointerType	InstantiateCudaBackProjection ()

ForwardProjectionPointerType	InstantiateCudaForwardProjection ()

ForwardProjectionPointerType	InstantiateCudaForwardProjection ()

BackProjectionPointerType	InstantiateCudaRayCastBackProjection ()

BackProjectionPointerType	InstantiateCudaRayCastBackProjection ()

virtual ForwardProjectionPointerType	InstantiateForwardProjectionFilter (int fwtype)

BackProjectionPointerType	InstantiateJosephBackAttenuatedProjection ()

BackProjectionPointerType	InstantiateJosephBackAttenuatedProjection ()

ForwardProjectionPointerType	InstantiateJosephForwardAttenuatedProjection ()

ForwardProjectionPointerType	InstantiateJosephForwardAttenuatedProjection ()

BackProjectionPointerType	InstantiateZengBackProjection ()

BackProjectionPointerType	InstantiateZengBackProjection ()

ForwardProjectionPointerType	InstantiateZengForwardProjection ()

ForwardProjectionPointerType	InstantiateZengForwardProjection ()

	IterativeConeBeamReconstructionFilter ()

	~IterativeConeBeamReconstructionFilter () override=default

Protected Attributes
AddFilterType::Pointer	m_AddFilter1

AddFilterType::Pointer	m_AddFilter2

BackProjectionImageFilter< TOutputImage, TOutputImage >::Pointer	m_BackProjectionFilter

BackProjectionImageFilter< TOutputImage, TOutputImage >::Pointer	m_BackProjectionFilterForConjugateGradient

CGOperatorFilterType::Pointer	m_CGOperator

ConjugateGradientFilterType::Pointer	m_ConjugateGradientFilter

DisplacedDetectorFilterType::Pointer	m_DisplacedDetectorFilter

ForwardProjectionImageFilter< TOutputImage, TOutputImage >::Pointer	m_ForwardProjectionFilterForConjugateGradient

MultiplyFilterType::Pointer	m_MultiplyFilter

SoftThresholdFilterType::Pointer	m_SoftThresholdFilter

SubtractFilterType::Pointer	m_SubtractFilter1

SubtractFilterType::Pointer	m_SubtractFilter2

MultiplyFilterType::Pointer	m_ZeroMultiplyFilter

Protected Attributes inherited from rtk::IterativeConeBeamReconstructionFilter< TOutputImage, TOutputImage >
double	m_AlphaPSF

BackProjectionType	m_CurrentBackProjectionConfiguration

ForwardProjectionType	m_CurrentForwardProjectionConfiguration

std::default_random_engine	m_DefaultRandomEngine

double	m_SigmaZero

double	m_StepSize

Private Attributes
unsigned int	m_AL_iterations { 10 }

float	m_Alpha { 1 }

float	m_Beta { 1 }

unsigned int	m_CG_iterations { 3 }

bool	m_DisableDisplacedDetectorFilter

ThreeDCircularProjectionGeometry::Pointer	m_Geometry

unsigned int	m_NumberOfLevels { 5 }

unsigned int	m_Order { 3 }

Additional Inherited Members
Protected Types inherited from rtk::IterativeConeBeamReconstructionFilter< TOutputImage, TOutputImage >
using	CPUImageType = typename itk::Image< typename TOutputImage ::PixelType, TOutputImage ::ImageDimension >

using	EnableCudaScalarAndVectorType = typename std::enable_if< !std::is_same< CPUImageType, ImageType >::value &&std::is_same< typename itk::PixelTraits< typename ImageType::PixelType >::ValueType, float >::value &&(itk::PixelTraits< typename ImageType::PixelType >::Dimension==1\|\|itk::PixelTraits< typename ImageType::PixelType >::Dimension==2\|\|itk::PixelTraits< typename ImageType::PixelType >::Dimension==3)>::type

using	DisableCudaScalarAndVectorType = typename std::enable_if< std::is_same< CPUImageType, ImageType >::value\|\|!std::is_same< typename itk::PixelTraits< typename ImageType::PixelType >::ValueType, float >::value\|\|(itk::PixelTraits< typename ImageType::PixelType >::Dimension !=1 &&itk::PixelTraits< typename ImageType::PixelType >::Dimension !=2 &&itk::PixelTraits< typename ImageType::PixelType >::Dimension !=3)>::type

using	EnableCudaScalarType = typename std::enable_if< !std::is_same< CPUImageType, ImageType >::value &&std::is_same< typename itk::PixelTraits< typename ImageType::PixelType >::ValueType, float >::value &&itk::PixelTraits< typename ImageType::PixelType >::Dimension==1 >::type

using	DisableCudaScalarType = typename std::enable_if< std::is_same< CPUImageType, ImageType >::value\|\|!std::is_same< typename itk::PixelTraits< typename ImageType::PixelType >::ValueType, float >::value\|\|itk::PixelTraits< typename ImageType::PixelType >::Dimension !=1 >::type

using	EnableVectorType = typename std::enable_if< itk::PixelTraits< typename ImageType::PixelType >::Dimension !=1 >::type

using	DisableVectorType = typename std::enable_if< itk::PixelTraits< typename ImageType::PixelType >::Dimension==1 >::type

Detailed Description

template<typename TOutputImage>
class rtk::ADMMWaveletsConeBeamReconstructionFilter< TOutputImage >

Implements the ADMM reconstruction with wavelets regularization.

This filter implements the operator A used in the conjugate gradient step of a reconstruction method based on compressed sensing. The method attempts to find the f that minimizes || Rf -p ||_2^2 + alpha * || W(f) ||_1, with R the forward projection operator, p the measured projections, and W the Daubechies wavelets transform. Note that since Daubechies wavelets are orthogonal, \( W^{T} = W^{-1} \) Details on the method and the calculations can be found on page 53 of

Mory, C. "Cardiac C-Arm Computed Tomography", PhD thesis, 2014. https://hal.inria.fr/tel-00985728/document

\( f_{k+1} \) is obtained by linear conjugate solving the following:

\[ ( R^T R + \beta I ) f = R^T p + \beta W^{-1} ( g_k + d_k ) \]

\( g_{k+1} \) is obtained by soft thresholding:

\[ g_{k+1} = ST_{ \frac{\alpha}{2 \beta} } ( W f_{k+1} - d_k ) \]

\( d_{k+1} \) is a simple subtraction:

\[ d_{k+1} = g_{k+1} - ( W f_{k+1} - d_k) \]

In ITK, it is much easier to store a volume than its wavelets decomposition. Therefore, we store \( g'_k = W^{-1} g_k \) and \( d'_k = W^{-1} d_k \) instead of \( g_k \) and \( d_k \). The above algorithm can therefore be re-written as follows:

\( f_{k+1} \) is obtained by linear conjugate solving the following:

\[ ( R^T R + \beta I ) f = R^T p + \beta ( g'_k + d'_k ) \]

\( g'_{k+1} \) is obtained by soft thresholding:

\[ g'_{k+1} = W^{-1} ( ST_{ \frac{\alpha}{2 \beta} } W( f_{k+1} - d'_k )) \]

\( d'_{k+1} \) is a simple subtraction:

\[ d'_{k+1} = g'_{k+1} - ( f_{k+1} - d'_k) \]

The wavelet decomposition and reconstruction steps are therefore performed only for soft thresholding.

Test:: rtkadmmwaveletstest.cxx

Author: Cyril Mory

Definition at line 143 of file rtkADMMWaveletsConeBeamReconstructionFilter.h.