Three-Dimensional SART Analysis for Muon Tomography

Sungchul Lee; Yun Gyeong Choi

doi:10.32390/ksmer.2021.58.5.380

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2021 Vol.58, Issue 5S Preview Page Next Page

Research Paper (Special Issue)

Three-Dimensional SART Analysis for Muon Tomography 뮤온 토모그래피 적용을 위한 3차원 SART 분석법 연구

31 October 2021. pp. 380-393

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Abstract

We developed an analysis program using the simultaneous algebraic reconstruction technique (SART) and applied it to projection data constructed using a three-dimensional Shepp–Logan model. To reduce the memory space and speed up the calculations, we used a compressed expression of the matrix, which saves only nonzero data. We compared the reconstructed images of SART with those of the simultaneous iterative reconstruction technique. This SART analysis can be applied to cosmic muon data and seismic data if the matrix is updated by ray tracing in the iteration process

Keywords

Three-dimensional

SART

muon tomography

compressed expression of a matrix

Shepp-Logan model

3차원 투영자료에 대한 SART 분석법을 개발하여 Shepp-Logan 모델 형태의 투영자료에 적용하여 영상재구성을 수행하였다. SART 계산에서 메모리 공간의 절약과 계산 속도를 높이기 위해 행렬의 값이 0이 아닌 경우만 메모리에 저장하는 압축표현 방식을 사용하였다. 재구성된 영상은 SIRT 분석법에 의해 재구성된 영상과 비교하였다. 본 연구에서 개발된 SART 분석법은 코스믹 뮤온 탐사 자료뿐 아니라, 반복과정 중 파선추적을 통해 행렬을 갱신하는 경우 탄성파 탐사 자료에도 적용이 가능하다.

키워드

3차원

SART

뮤온 토모그래피

압축표현 행렬

Shepp-Logan 모델

References

Ambrose, J. and Hounsfield, G., 1973. Computerized transverse axial tomography, British Journal of Radiology, 46, p.148-149. 10.1259/0007-1285-46-552-10164757352

Andersen, A.H. and Kak, A.C., 1984. Simultaneous algebraic reconstruction technique(SART): A superior implementation of the art algorithm, Ultrasonic Imaging, 6, p.81-94. 10.1177/0161734684006001076548059

Bonechi, L., D'Alessandro, R., and Giammanco, A., 2020. Atmospheric muons as an imaging tool, Reviews in Physics, 5, 100038p. 10.1016/j.revip.2020.100038

Comack, A.M., 1963. Representation of a function by its line integrals with some radiological application, Journal of Applied Physics, 34, p.2722-2727. 10.1063/1.1729798

Comack, A.M., 1964. Representation of a function by its line integrals with some radiological application II, Journal of Applied Physics, 35, p.2908-2913. 10.1063/1.1713127

D'Alessandro, R., Ambrosino, F., Baccani, G., Bonechi, L., Bongi, M., Caputo, A., Ciaranfi, R., Cimmino, L., Ciulli, V., D'Errico, M., Giudicepietro, F., Gonzi, S., Macedonio, G., Masone, V., Melon, B., Mori, N., Noli, P., Orazi, M., Passeggio, P., Peluso, R., Saracino, G., Scognamiglio, L., Strolin, P., Vertechi, E., and Viliani, L., 2018. Volcanoes in Italy and the role of muon radiography, Philosophical Transactions a Royal Society A, 377(2137):20180050. 10.1098/rsta.2018.005030530551PMC6335311

Dempster, A.P., Laird, N.M., and Rubin, D.B., 1977. Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society B, 39(1), p.1-38. 10.1111/j.2517-6161.1977.tb01600.x

Dines, K.A. and Lytle.R.J., 1979, Computerized geophysical tomography, Proc. IEEE, 67, p.1065-1073. 10.1109/PROC.1979.11390

Feldkamp, L.A., Davis, L.C., and Kress, J.W., 1984. Practical cone-beam algorithm, Journal of the Optical Society of America A, 1(6), p.612-619. 10.1364/JOSAA.1.000612

Gordon, R., Bender, R., and Herman, G.T., 1970. Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography, Journal of Theoretical Biology, 29(3), p.471-481. 10.1016/0022-5193(70)90109-8

Hestenes, M.R. and Stiefel, E., 1952. Methods of Conjugate Gradients for Solving Linear Systems, Journal of Research of the National Bureau of Standards, 49(6), p.409-436. 10.6028/jres.049.044

Hyun, B.K., Lim, H.R. and Lee, H.Y., 1992. Applicability of the Seismic Sraight Ray Tomography for the Image Reconstruction of the Subsurface Structure, Journal of The Korean Institute of Mineral and Energy Resources Engineers, 29, p.245-254.

Jonkmans, G., Anghel, V.N.P., Jewett, C., and Thompson, M., 2012. Nuclear Waste Imaging and Spent Fuel Verification by Muon Tomography, Annals of Nuclear Energy, 53, p.267-273. 10.1016/j.anucene.2012.09.011

Lee, H.Y., 1990. Geotomographic Inversion using CG, SIRT and DLSQ Methods, Journal of The Korean Institute of Mineral and Energy Resources Engineers, 27, p.222-233.

Liu, Z., Chatzidakis, S., Scaglione, J.M., Liao, C., Yang, H., and Hayward, J.P., 2019, Muon tracing and image reconstruction algorithms for cosmic muon computed tomography, IEEE Transactions on Image Processing, 28(1), p.426-435. 10.1109/TIP.2018.286966730222560

Marteau, J., Carlus, B., Gibert, D., Ianigro, J.C., Jourde, K., Kergosien, B., and Rolland P., 2016. Muon tomography applied to active volcanoes, Proceedings of Science, International Conference on New Photo-detectors, PhotoDet2015, 6-9 Jul 2015, Moscow, Russia. 10.22323/1.252.000427117017

Morishima, K., Kuno M., Nishio, A., Kitagawa, N., Manabe, Y., Moto, M., Takasaki, F., Fujii, H., Satoh, K., Kodama, H., Hayashi, K., Odaka, S., Procureur, S., Attié, D., Bouteille, S., Calvet, D., Filosa, C., Magnier, P., Mandjavidze, I., Riallot, M., Marini, B., Gable, P., Date, Y., Sugiura, M., Elshayeb, Y., Elnady, T., Ezzy, M., Guerriero, E., Steiger, V., Serikoff, N., Mouret, J.B., Charlès, B., Helal, H., and Tayoubi, M., 2017. Discovery of a big void in Khufu's Pyramid by observation of cosmic-ray muons, Nature, 552, p.386-390. 10.1038/nature2464729160306

Paige, C.C. and Saunders, M.A., 1982. LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Transactions on Mathematical Software, 8, p.43-71. 10.1145/355984.355989

Rosenfeld, A. and Kak, A.C., 1982. Computer Science and Applied Mathematics: Digital Picture Processing(2nd Ed.), Vol. 1, Academic Press, Orlando, USA, p.353-413.

Shepp, L.A., and Logan, B.F., 1974a. The Fourier reconstruction head section Transmissions, IEEE Transactions on Nuclear Science, 21(1), p.21-43. 10.1109/TNS.1974.6499235

Shepp, L. A., and Logan, B. F., 1974b. Reconstructing interior head tissue from X-ray transmissions, IEEE Transactions on Nuclear Science, 21(1), p.228-236. 10.1109/TNS.1974.4327466

Sorzano, C.O.S., Vargas, J., Oton, J. de la Rosa-Trevin, J.M., Vilas, J.L., Kazemi, M., Melero, R., del Caño, L., Cuenca, J., Conesa, P., Gómez-Blanco, J., Marabini, R. and Carazo, J.M., 2017. A survey of the use of iterative reconstruction algorithms in electron microscopy, BioMed Research International, 2017, 6482567. 10.1155/2017/648256729312997PMC5623807

Tanaka, H.K.M., 2018. Japanese volcanoes visualized with muography, Philosophical Transactions a Royal Society A, 377:20180142. 10.1098/rsta.2018.014230530547

Tanaka, H.K.M., Taira, H., Uchida, T., Tanaka, M., Takeo, M., Ohminato, T., Aoki, Y., Nichitama, R., Shoji, D., and Tsuiji, H., 2010. Three-dimensional computational axial tomography scan of a volcano with cosmic ray muon radiography, Journal of Geophysical Research, 115, B12332p. 10.1029/2010JB007677

Van der Sluis, A. and van der Vorst, H.A., 1990. SIRT- and CG-type methods for iterative solution of sparse linear least-squares problems, Linear Algebra and its Applications, 120, p.257-303. 10.1016/0024-3795(90)90215-X

Information

Publisher :The Korean Society of Mineral and Energy Resources Engineers
Publisher(Ko) :한국자원공학회
Journal Title :Journal of the Korean Society of Mineral and Energy Resources Engineers
Journal Title(Ko) :한국자원공학회지
Volume : 58
No :5
Pages :380-393
Received Date : 2021-08-06
Revised Date : 2021-09-03
Accepted Date : 2021-10-26
DOI :https://doi.org/10.32390/ksmer.2021.58.5.380

Journal of the Korean Society of Mineral and Energy Resources Engineers ISSN:2288-0291(Print) 2288-2790(Online) 한국자원공학회지

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