# System matrix computation for iterative reconstruction algorithms in SPECT based on direct measurements

Damian Borys; Katarzyna Szczucka-Borys; Kamil Gorczewski

International Journal of Applied Mathematics and Computer Science (2011)

- Volume: 21, Issue: 1, page 193-202
- ISSN: 1641-876X

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topDamian Borys, Katarzyna Szczucka-Borys, and Kamil Gorczewski. "System matrix computation for iterative reconstruction algorithms in SPECT based on direct measurements." International Journal of Applied Mathematics and Computer Science 21.1 (2011): 193-202. <http://eudml.org/doc/208033>.

@article{DamianBorys2011,

abstract = {A method for system matrix calculation in the case of iterative reconstruction algorithms in SPECT was implemented and tested. Due to a complex mathematical description of the geometry of the detector set-up, we developed a method for system matrix computation that is based on direct measurements of the detector response. In this approach, the influence of the acquisition equipment on the image formation is measured directly. The objective was to obtain the best quality of reconstructed images with respect to specified measures. This is indispensable in order to be able to perform reliable quantitative analysis of SPECT images. It is also especially important in non-hybrid gamma cameras, where not all physical processes that disturb image acquisition can be easily corrected. Two experiments with an 131 I point source placed at different distances from the detector plane were performed allowing the detector response to be acquired as a function of the point source distance. An analytical Gaussian function was fitted to the acquired data in both the one- and the two-dimensional case. A cylindrical phantom filled with a water solution of 131 I containing a region of “cold” spheres as well as a uniform solution (without any spheres) was used to perform algorithm evaluation. The reconstructed images obtained by using four different of methods system matrix computation were compared with those achieved using reconstruction software implemented in the gamma camera. The contrast of the spheres and uniformity were compared for each reconstruction result and also with the ranges of those values formulated by the AAPM (American Association of Physicists in Medicine). The results show that the implementation of the OSEM (Ordered Subsets Expectation Maximization) algorithm with a one-dimensional fit to the Gaussian CDR (Collimator-Detector Response) function provides the best results in terms of adopted measures. However, the fit of the two-dimensional function also gives satisfactory results. Furthermore, the CDR function has the potential to be applied to a fully 3D OSEM implementation. The lack of the CDR in system matrix calculation results in a very noisy image that cannot be used for diagnostic purposes.},

author = {Damian Borys, Katarzyna Szczucka-Borys, Kamil Gorczewski},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {SPECT; iterative reconstruction; quantitative imaging; nuclear medicine imaging},

language = {eng},

number = {1},

pages = {193-202},

title = {System matrix computation for iterative reconstruction algorithms in SPECT based on direct measurements},

url = {http://eudml.org/doc/208033},

volume = {21},

year = {2011},

}

TY - JOUR

AU - Damian Borys

AU - Katarzyna Szczucka-Borys

AU - Kamil Gorczewski

TI - System matrix computation for iterative reconstruction algorithms in SPECT based on direct measurements

JO - International Journal of Applied Mathematics and Computer Science

PY - 2011

VL - 21

IS - 1

SP - 193

EP - 202

AB - A method for system matrix calculation in the case of iterative reconstruction algorithms in SPECT was implemented and tested. Due to a complex mathematical description of the geometry of the detector set-up, we developed a method for system matrix computation that is based on direct measurements of the detector response. In this approach, the influence of the acquisition equipment on the image formation is measured directly. The objective was to obtain the best quality of reconstructed images with respect to specified measures. This is indispensable in order to be able to perform reliable quantitative analysis of SPECT images. It is also especially important in non-hybrid gamma cameras, where not all physical processes that disturb image acquisition can be easily corrected. Two experiments with an 131 I point source placed at different distances from the detector plane were performed allowing the detector response to be acquired as a function of the point source distance. An analytical Gaussian function was fitted to the acquired data in both the one- and the two-dimensional case. A cylindrical phantom filled with a water solution of 131 I containing a region of “cold” spheres as well as a uniform solution (without any spheres) was used to perform algorithm evaluation. The reconstructed images obtained by using four different of methods system matrix computation were compared with those achieved using reconstruction software implemented in the gamma camera. The contrast of the spheres and uniformity were compared for each reconstruction result and also with the ranges of those values formulated by the AAPM (American Association of Physicists in Medicine). The results show that the implementation of the OSEM (Ordered Subsets Expectation Maximization) algorithm with a one-dimensional fit to the Gaussian CDR (Collimator-Detector Response) function provides the best results in terms of adopted measures. However, the fit of the two-dimensional function also gives satisfactory results. Furthermore, the CDR function has the potential to be applied to a fully 3D OSEM implementation. The lack of the CDR in system matrix calculation results in a very noisy image that cannot be used for diagnostic purposes.

LA - eng

KW - SPECT; iterative reconstruction; quantitative imaging; nuclear medicine imaging

UR - http://eudml.org/doc/208033

ER -

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