Reconstruction of parameters of a set of radiant points from their images
Matematičeskie trudy, Tome 26 (2023) no. 2, pp. 62-85.

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Within the framework of geometric tomography, inverse problems of photometry, wave optics, and discrete tomography, we study questions on reconstruction of the spatial location and luminosity of a discrete distribution of radiant sources from its images obtained with the use of a small number of optical systems. We analyze the problem on finding geometric parameters of such a distribution and describe sources of ambiguity. We consider the inverse problem on reconstruction of a discrete distribution that consists of incoherent and monochromatic sources and suggest uniqueness criteria for its solution. We also suggest a constructive approach to numerical solution of the inverse problem on reconstruction of the coordinates and luminosity of a family of radiant pinpoint sources from their images.
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E. Yu. Derevtsov. Reconstruction of parameters of a set of radiant points from their images. Matematičeskie trudy, Tome 26 (2023) no. 2, pp. 62-85. http://geodesic.mathdoc.fr/item/MT_2023_26_2_a3/

[1] Dzh. Gudmen, Vvedenie v fure-optiku, Mir, M., 1970

[2] E. Yu. Derevtsov, “Ob odnoi zadache volnovoi optiki”, Vychislitelnye problemy matematicheskikh zadach geofiziki, Vychislitelnyi tsentr SO AN SSSR, Novosibirsk, 1977, 36–47

[3] E. Yu. Derevtsov, Chislennoe reshenie nekotorykh zadach volnovoi optiki, Preprint No 275, VTs SO AN SSSR, Novosibirsk, 1981

[4] V. R. Kireitov, “O zadache vosstanovleniya opticheskoi poverkhnosti po ee izobrazheniyam”, Funkts. analiz i ego pril., 10:3 (1975), 45–54

[5] V. R. Kireitov, “O nekotorykh obratnykh zadachakh volnovoi optiki. Ch. 1”, Matematicheskie problemy geofiziki, 6, Vychislitelnyi tsentr SO AN SSSR, Novosibirsk, 1975, 167–210

[6] V. R. Kireitov, “O nekotorykh obratnykh zadachakh volnovoi optiki. Ch. 2”, Matematicheskie problemy geofiziki, 6, Vychislitelnyi tsentr SO AN SSSR, Novosibirsk, 1975, 90–121

[7] V. R. Kireitov, Obratnye zadachi fotometrii, Vychislitelnyi tsentr SO AN SSSR, Novosibirsk, 1983

[8] M. M. Lavrentev, V. S. Ladyzhets, “Ob odnoi obratnoi zadache geometricheskoi optiki”, Dokl. AN SSSR, 269:6 (1983), 1313–1315 | MR | Zbl

[9] M. M. Lavrentev, E. K. Derevtsov, V. A. Sharafutdnnov, “Ob opredelenii opticheskogo tela, nakhodyaschegosya v odnorodnoi srede, po ego izobrazheniyam”, Dokl. AN SSSR, 260:4 (1981), 799–803 | MR | Zbl

[10] A. N. Lobanov, Fotogrammetriya, Uchebnik dlya vuzov, 2-e izd., Nedra, M., 1984

[11] A. I. Obnralov, A. N. Limonov, L. A. Gavrilova, Fotogrammetriya i distantsionnoe zondirovanie, KolosS, M., 2006

[12] G. Khermen, Vosstanovlenie izobrazhenii po proektsiyam: Osnovy, rekonstruktivnoi tomografii, Mir, M., 1983 | MR

[13] A. Alpers, P. Gritzmann, “On Stability, Error Correction, and Noise Compensation in Discrete Tomography”, SIAM J. Discrete Math., 20:1 (2006), 227–239 | DOI | MR | Zbl

[14] E. Yu. Derevtsov, “Ghost distributions in the eone-beam tomography”, J. Inverse Ill-Posed Probl., 5:5 (1997), 411–426 | DOI | MR | Zbl

[15] R. J. Gardner, Geometric Tomography, 2nd edition, Cambridge University Press, New York, 2006 | MR | Zbl

[16] G. T. Herman, A. Kuba, Advances in Discrete Tomography and Its Applications, Birkhauser Boston, Boston, 2007 | MR | Zbl

[17] A. K. Louis, “Ghosts in tomography the null space of the radon transform”, Math. Methods Appl. Sci., 3:1 (1981), 1–10 | DOI | MR | Zbl

[18] A. K. Louis, “Nonuniqueness in inverse Radon problems: the frequency distribution of the ghosts”, Math. Z., 185:3 (1984), 429–440 | DOI | MR | Zbl

[19] A. K. Louis, “Orthogonal function series expansions and the null space of the radon transform”, SI AM J. Math. Anal., 15 (1984), 621–633 | DOI | MR | Zbl

[20] V. A. Sharafutdinov, “Uniqueness theorems for the exponential X-ray transform”, J. Inverse Ill-Posed Probl., 1:4 (1993), 355–372 | DOI | MR | Zbl

[21] K. T. Smith, D. G. Solmon, S. L. Wagner, “Practical and mathematical aspects of the problem of reconstructing objects from radiographs”, Bull. Amer. Math. Soc., 83:11 (1977), 1227–1270 ; 12, 3905–3916 | DOI | MR | Zbl

[22] B. van Dalen, “Stability results for uniquely determined sets from two directions in discrete tomography”, Discrete Mathematics, 309 (2009) | MR