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Damian Borys, Katarzyna Szczucka-Borys and Kamil Gorczewski

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

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.

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Jyun-Jhe Chou, Chi-Sheng Shih, Wei-Dean Wang and Kuo-Chin Huang

References Administration on Aging (2015). A Profile of Older Americans: 2015 , US Department of Health and Human Services, . Alemdar, H. and Ersoy, C. (2010). Wireless sensor networks for healthcare: A survey, Computer Networks 54 (15): 2688–2710. Bourke, A.K., Ihlen, E.A., Van de Ven, P., Nelson, J. and Helbostad, J.L. (2016). Video analysis validation of a real-time physical activity detection algorithm based on a single waist mounted tri-axial accelerometer sensor, IEEE 38th Annual

Open access

Tadeusz Kaczorek

References Bistritz, Y. (2003). A stability test for continuous-discrete bivariate polynomials, Proceedings of the International Symposium on Circuits and Systems , Vol. 3, pp. 682-685. Busłowicz, M. (2010a). Stability and robust stability conditions for a general model of scalar continuous-discrete linear systems, Pomiary, Automatyka, Kontrola 56(2): 133-135. Busłowicz, M. (2010b). Robust stability of the new general 2D model of a class of continuous-discrete linear systems

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Fengxiang Zhang, Yanfeng Zhai and Jianwei Liao

). Control robotics: The procedural control of physical processes, IFIP Congress, Stockholm, Sweden , pp. 807–813. Devi, M. (2003). An improved schedulability test for uniprocessor periodic task systems, Proceedings of the 15th Euromicro Conference on Real-Time Systems, Porto, Portugal , pp. 23–30. Ghazalie, T.M. and Baker, T.P. (1995). Aperiodic servers in a deadline scheduling environment, Real-Time Systems 9 (1): 31–67. Harbour, M.G. and Palencia, J.C. (2003). Response time analysis for tasks scheduled under EDF within fixed priorities, 24th IEEE

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Mikołaj Busłowicz and Andrzej Ruszewski

, Proceedings of the IFAC Workshop on Time-Delay Systems (TDS 2003), Rocquencourt, France , (CD-ROM). Gałkowski, K., Rogers, E., Paszke, W. and Owens, D. H. (2003). Linear repetitive process control theory applied to a physical example, International Journal of Applied Mathematics and Computer Science   13 (1): 87-99. Guiver, J. P. and Bose, N. K. (1981). On test for zero-sets of multivariate polynomials in noncompact polynomials, Proceedings of the IEEE   69 (4): 467-469. Hespanha, J. (2004

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Cili Zuo, Lianghong Wu, Zhao-Fu Zeng and Hua-Liang Wei

, K., Thiele, L., Laumanns, M. and Zitzler, E. (2005). Scalable Test Problems for Evolutionary Multiobjective Optimization, Springer, London. Denysiuk, R., Costa, L., Santo, I.E. and Matos, J.C. (2015). MOEA/PC: Multiobjective evolutionary algorithm based on polar coordinates, International Conference on Evolutionary Multi-Criterion Optimization, Guimar˜aes, Portugal, pp. 141-155. Derrac, J., García, S., Molina, D. and Herrera, F. (2011). A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing

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Anna Papiez, Christophe Badie and Joanna Polanska

., Dezfooli, S.R., Zandonà, A., Jurman, G. and Furlanello, C. (2018). Multi-omics integration for neuroblastoma clinical endpoint prediction, Biology Direct 13 (1): 5. Guidi, G., Maffei, N., Vecchi, C., Gottardi, G., Ciarmatori, A., Mistretta, G. M., Mazzeo, E., Giacobazzi, P., Lohr, F. and Costi, T. (2017). Expert system classifier for adaptive radiation therapy in prostate cancer, Australasian Physical & Engineering Sciences in Medicine 40 (2): 337–348. Jagga, Z. and Gupta, D. (2015). Machine learning for biomarker identification in cancer research

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Ibrahima N’Doye, Mohamed Darouach, Holger Voos and Michel Zasadzinski

Science and Numerical Simulation 15 (2): 384-393. Petráš, I. (2011). Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation , Springer, Berlin. Petráš, I., Chen, Y. and Vinagre, B. (2004). Robust stability test for interval fractional-order linear systems, in V.Blondel and A. Megretski (Eds.), Unsolved Problems in the Mathematics of Systems and Control , Vol. 38, Princeton University Press, Princeton, NJ, pp. 208-210. Podlubny, I. (1999). Fractional Differential Equations , Academic, New York, NY

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Dariusz Uciński and Maciej Patan

of Thermal Sciences   41 : 536-546. Lehmann, E. L. and Romano, J. P. (2005). Testing Statistical Hypotheses , 3rd Edn., Springer-Verlag. Ljung, L. (1999). System Identification: Theory for the User , 2nd Edn., Prentice Hall, Upper Saddle River, NJ. Maksimov, V. I. (2000). Problems of Dynamic Input Reconstruction of Infinite-Dimensional Systems , Russian Academy of Sciences Press, Ekaterinburg, (in Russian). Martínez, S. and Bullo, F. (2006). Optimal sensor

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Krzysztof Moliński, Anita Dobek and Kamila Tomaszyk

significance of attribute interaction. Proc. 21st International Conference on Machine Learning. Banff, Canada. Kang G., Yue W., Zhang J., Cui Y., Zuo Y., Zhang D. (2008): An entropy-based approach for testing genetic epistasis underlying complex diseases. Journal of Theoretical Biology 250: 362-374. Kullback S., Leibler R.A. (1951): On information and sufficiency. Annals of Mathematical Statistics 22(1): 79-86. Matsuda H. (2000): Physical nature of higher-order mutual information. Intrinsic correlation and frustration. Physical