Discrete scattering centers reconstruction problem on a limited set of projections | Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitelnaja tehnika i informatika – Tomsk State University Journal of Control and Computer Science. 2012. № 56.

Discrete scattering centers reconstruction problem on a limited set of projections

We consider the actual problem of reconstruction the maximum subset of points in R on a limited set of two-dimensional projections. This problem arises naturally in applications of physical hydrodynamics to real optical diagnostics of liquid and gas by measuring the instantaneous velocity fields in the bulk flow. During the experimental data processing is solved the problem of reconstruction the internal structure of the scattering medium which is a set of discrete small particles, moving with the speed closely like to the speed of a continuous medium. The instantaneous flow rate is determined by the change in the position of the particles over time. We prove a theorem that allows us to answer the question of the sufficiency of the changes to uniquely identify a set of two-dimensional set of its projections. Iterative algorithm is proposed to restore the maximum set by its set of projections.

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Keywords

анемометрия по изображениям частиц, оптическая томография, обратные задачи, particle image velocimetry (PIV), optical tomography, inverse problems

Authors

Name	Organization	E-mail
Dedok Vasily A.	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences (Novosibirsk)	dedok@math.nsc.ru
Tokarev Mikhail P.	Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences (Novosibirsk)	mtokarev@itp.nsc.ru
Bondarenko Anatoly N.	Novosibirsk State University; Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences (Novosibirsk)	bondarenkoan1953@mail.ru

Всего: 3

References

Хермен Г. Т. Восстановление изображений по проекциям. Основы реконструктивной томографии. М.: Мир, 1983.

Лаврентьев М.М., Зеркаль С.М., Трофимов О.Е. Численное моделирование в томографии и условно-корректные задачи. Новосибирск: Изд-во ИДМИ НГУ, 1999.

Raff el M., Willet C.E., Were ley S.T., Kompenhans J. Particle Image Velocimetry. Practical Guide. Berlin: Springer, 2007.

Elsinga G.E., Scarano F., Wieneke B., van Oudheusden B.W. Tomagraphic particle image ve-locimetry // Exp. Fluids. 2006. V. 41. P. 933-947.

Бильский А.В., Ложкин В.А., Маркович Д.М. и др. Оптимизация и тестирование томографического метода измерения скорости в объеме потока // Теплофизика и аэромеханика. 2011. Т. 18. № 4. C. 555-566.

Maas H.G., Gruen A.,Papantoniou,D. Particle tracking velocimetry in tree-dimentional flows // Exp. Fluids. 1993. V. 15. P. 133-146.

Novara M., Scarano F. Performances of motion tracking enhanced Tomo-PIV on turbulent shear flows // Exp. Fluids. 2012. V. 52. P. 1027-1041.

Wieneke B. Iterative reconstruction of volumetric particle distribution // Proc. 9th International Symposium on Particle Image Velocimetry, July 21-23, 2011, Kobe, Japan.