Collaboration diagram for Singles rates etc:

Files
file	randoms_from_singles.cxx
	Implementation of stir::randoms_from_singles.

file	SinglesRates.cxx
	Implementation of stir::FrameSinglesRates and stir::SinglesRates.

file	SinglesRatesForTimeFrames.cxx
	Implementation of stir::SinglesRatesForTimeFrames.

file	SinglesRatesForTimeSlices.cxx
	Implementation of stir::SinglesRatesForTimeSlices.

file	SinglesRatesFromECAT7.cxx
	Implementation of stir::ecat::ecat7::SinglesRatesFromECAT7.

file	SinglesRatesFromGEHDF5.cxx
	Implementation of stir::GE::RDF_HDF5::SinglesRatesFromGEHDF5.

file	SinglesRatesFromSglFile.cxx
	Implementation of stir::ecat::ecat7::SinglesRatesFromECAT7.

file	randoms_from_singles.h
	declare stir:randoms_from_singles

file	SinglesRates.h
	Declaration of class stir::SinglesRates.

file	SinglesRates.inl
	Implementation of class stir::SinglesRates.

file	SinglesRatesForTimeFrames.h
	Declaration of class stir::SinglesRatesForTimeFrames.

file	SinglesRatesForTimeSlices.h
	Declaration of class stir::SinglesRatesForTimeSlices.

file	SinglesRatesFromECAT7.h
	Declaration of class stir::ecat::ecat7::SinglesRatesFromECAT7.

file	SinglesRatesFromGEHDF5.h
	Declaration of class stir::GE::RDF_HDF5::SinglesRatesFromGEHDF5.

file	SinglesRatesFromSglFile.h
	Declaration of class stir::SinglesRatesFromSglFile.

Classes
class	stir::FrameSinglesRates
	A single frame of singles information. More...

class	stir::SinglesRates
	The base-class for using singles info. More...

class	stir::SinglesRatesForTimeFrames
	A class for singles rates that are recorded in time frames. More...

class	stir::SinglesRatesForTimeSlices
	A class for singles that are recorded at equal time intervals. More...

class	stir::ecat::ecat7::SinglesRatesFromECAT7
	A class that extracts singles info from an ECAT7 sinogram file. More...

class	stir::GE::RDF_HDF5::SinglesRatesFromGEHDF5
	A class for reading singles over the number of time samples from an GE HDF5 .BLF listmode file format. More...

class	stir::ecat::ecat7::SinglesRatesFromSglFile
	A class for reading/writing singles from an ECAT7 .sgl file. More...

Functions
void	stir::randoms_from_singles (ProjData &proj_data, const SinglesRates &singles, float coincidence_time_window=-1.F, float radionuclide_halflife=-1.F)
	Estimate randoms from singles (RFS)

Detailed Description

Function Documentation

◆ randoms_from_singles()

void stir::randoms_from_singles	(	ProjData &	proj_data,
		const SinglesRates &	singles,
		float	coincidence_time_window = -1.F,
		float	radionuclide_halflife = -1.F )

Estimate randoms from singles (RFS)

Parameters

[in,out]	proj_data	Projection data to store output. It needs to be properly initialised with sizes etc. If coincidence_time_window or radionuclide_halflife are invalid, they will be determined from the proj_data.
[in]	singles	Input value for RFS
[in]	coincidence_time_window	Scanner coincidence window (in secs). Deprecated.
[in]	radionuclide_halflife	half-life. Deprecated.

This uses the formula $R_{ij}= \tau S_i S_j$ (with $\tau$ the coincidence_time_window) for finding the randoms-rate in terms of the singles-rates. The function then takes duration properly into account using the following procedure. This uses isotope_halflife in the computation of $\lambda$ . Default value is -1 and the function will extract isotope_halflife from proj_data. If set, will use the passed value.

We actually have total counts in the singles for sinograms and need total counts in the randoms. Assuming the radioactivity distribution is stationary and only decays, and dropping indices , we get

$R_{ij}(t) = \tau * S_i(0) S_j(0) exp (-2 \lambda t)$

Integrating over time, and writing $r$ for the integral of $R$ etc

$r_{ij} = \tau S_i(0) S_j(0) \int_{t_1}^{t_2} dt\,exp (-2 \lambda t)$

converting that to total singles $s$ in the time frame, we get

$r_{ij} = \tau s_i s_j \frac{ \int_{t_1}^{t_2} dt\,exp (-2 \lambda t)}{\left(\int_{t1}^{t2} dt\,exp (-\lambda t)\right)^2}$

For more details, see: Stearns, C. W., McDaniel, D. L., Kohlmyer, S. G., Arul, P. R., Geiser, B. P., & Shanmugam, V. (2003). Random coincidence estimation from single event rates on the Discovery ST PET/CT scanner. 2003 IEEE Nuclear Science Symposium. Conference Record (IEEE Cat. No.03CH37515), 5, 3067-3069. https://doi.org/10.1109/NSSMIC.2003.1352545

Todo: Dead-time is currently completely ignored.

References decay_correction_factor(), stir::ExamData::get_exam_info_sptr(), stir::Radionuclide::get_half_life(), stir::DataWithProjDataInfo::get_proj_data_info_sptr(), stir::ExamInfo::get_radionuclide(), stir::SinglesRates::get_singles(), info(), randoms_from_singles(), and square().

Referenced by randoms_from_singles().

Files

Classes

Functions

Detailed Description

Function Documentation

◆ randoms_from_singles()