Implementation of the Relative Difference penalty potential. More...

#include "stir/recon_buildblock/GibbsRelativeDifferencePenalty.h"

Public Member Functions
__host__ __device__ double	value (const elemT val_center, const elemT val_neigh, int z, int y, int x) const
	Method for computing the potential value.

__host__ __device__ double	derivative_10 (const elemT val_center, const elemT val_neigh, int z, int y, int x) const
	Method for computing the first derivative with respect to val_center.

__host__ __device__ double	derivative_20 (const elemT val_center, const elemT val_neigh, int z, int y, int x) const
	Method for computing the second derivative with respect to val_center.

__host__ __device__ double	derivative_11 (const elemT val_center, const elemT val_neigh, int z, int y, int x) const
	Method for computing the mixed second derivative.

void	initialise_keymap (KeyParser &parser)
	Method for setting up parsing additional parameters.

void	set_defaults ()
	Set default values for potential-specific parameters.

Static Public Member Functions
static bool	is_convex ()
	method to indicate whether the the prior defined by this potential is convex

Public Attributes
float	gamma

float	epsilon

Detailed Description

template<typename elemT>
class stir::RelativeDifferencePotential< elemT >

Implementation of the Relative Difference penalty potential.

The prior energy is:

$\sum_{r,dr} \kappa_{r} \kappa_{r+dr} w_{dr} \frac{(\lambda_r - \lambda_{r+dr})^2}{2(\lambda_r + \lambda_{r+dr} + \gamma |\lambda_r - \lambda_{r+dr}| + \epsilon)}$

Where:

$\lambda_r$ and $\lambda_{r+dr}$ are pixel values at positions and
$\gamma$ is a smoothing parameter for the prior (default: 2.0)
$\epsilon$ prevents division by zero (default: 1e-7)
$w_{dr}$ are distance-dependent weights
$\kappa$ provides spatially-varying penalty weights (optional)

Warning: Only well-defined for non-negative voxel values. With $\epsilon=0$ , gradient algorithms may have issues near zero values, as the Hessian becomes singular.

See also: Nuyts et al., "A Concave Prior Penalizing Relative Differences for Maximum-a-Posteriori Reconstruction in Emission Tomography," IEEE TNS, vol. 49(1), pp. 56-60, 2002.

The documentation for this class was generated from the following file:

/home/kris/devel/STIRdistrib/STIR/src/include/stir/recon_buildblock/GibbsRelativeDifferencePenalty.h

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description