Apodization of Black Holes in Super-Resolution Problems

Evgeni Nikolaevich Terentiev; Irina Igorevna Farshakova; Nikolay Evgenyevich Shilin-Terentyev

doi:doi:10.11648/j.ajaa.20190703.11

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Apodization of Black Holes in Super-Resolution Problems

Evgeni Nikolaevich Terentiev, Irina Igorevna Farshakova, Nikolay Evgenyevich Shilin-Terentyev

Published in American Journal of Astronomy and Astrophysics (Volume 7, Issue 3)

Received: 29 June 2019 Accepted: 31 July 2019 Published: 20 October 2019

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Abstract

Methods for identifying hidden objects are usually associated with the term apodization. The problem definitions of super-resolution must begin with the choice of the corresponding hidden object — the working discrete model of Apparatus Function (AF). With apodization such Black Holes, we will associate the mathematical invers problem of choosing working AFs with reversible R=O^-1 and a small inverse norm Nor (R)=||R||. The apodization setting of super-resolution tasks, the indication of objects arise in the analysis of the Characteristics of Circumstances (CC) of the O AF models. The article provides examples of demonstration of CС with the choice of a discrete model of AF O with the usual inversions R=O^-1 and without using a priori information about the type of solutions, as is customary in the regularization method [1]. The latter circumstance allowed us to solve the actual problem of the Super-Resolution of the image of the Black Hole Powehi shadow on low-accuracy data [16].

Published in	American Journal of Astronomy and Astrophysics (Volume 7, Issue 3)
DOI	10.11648/j.ajaa.20190703.11
Page(s)	39-47
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Mathematical Apodization, Apparatus Function, Invers Problems, Modulation Transfer Function, Conditionality, Invertibility Indicator

References

[1]	A. N. Tikhonov, M. V. Ufimtsev “Statistical processing of experimental results”, Moscow University Press, 1988 (in Russian).
[2]	Evgeni N. Terentiev, Nikolay E. Terentiev, M. V. Lomonosov Moscow State Univ. (Russia), Applications of pointed ultra-resolution method in colour imaging, published in Proceedings Volume 5817: Visual Information Processing XIV, May 2005, Available on the SPIE Digital Library.
[3]	Evgeni N. Terentiev, M. V. Lomonosov Moscow State Univ. (Russia); Nikolai E. Terentiev, XSIA (Russia); Fedor V. Shugaev, M. V. Lomonosov Moscow State Univ. (Russia), Inside the ultra-resolution method, published in Proceedings Volume 5574: Remote Sensing for Environmental Monitoring, GIS Applications, and Geology IV, October 2004, Available on the SPIE Digital Library.
[4]	Evgeni N. Terentiev, M. V. Lomonosov Moscow State Univ. (Russia); N. E. Terentiev, Quest Software Inc. (Russia), Characterization of ultra-resolution method, published in Proceedings Volume 6246: Visual Information Processing XV, May 2006 • View Abstract, Available on the SPIE Digital Library.
[5]	Evgeni N. Terentiev, M. V. Lomonosov Moscow State Univ. (Russia); Nikolay E. Terentiev, Quest Software Inc. (Russia), Ultra-resolution and indication of objects, published in Proceedings Volume 6211: Passive Millimeter-Wave Imaging Technology IX, May 2006 View Abstract, Available on the SPIE Digital Library.
[6]	Evgeni N. Terentiev, Nikolai E. Terentiev, M. V. Lomonosov Moscow State Univ. (Russia), Superresolution when PSF is indefinite, published in Proceedings Volume 4388: Visual Information Processing X, August 2001, Available on the SPIE Digital Library.
[7]	Terentiev E. N., Terentyev N. E. CHARACTERISTICS OF ADEQUACY OF MODELS OF MEASURING - COMPUTING SYSTEMS, Proceedings of the ХIХ International Forum on problems of science, technology and education, p. 95-97 (2015) (in Russian).
[8]	Terentyev E. N., Terentyev N. E. PROBLEMS OF MULTI-BEAM MEASURING - COMPUTING SYSTEMS, Proceedings of the ХIХ International Forum on problems of science, technology and education, p. 94-95 (2015) (in Russian).
[9]	Terentiev E. N., Terentyev N. E. ADEQUATE SETTINGS OF RAY CREST IN RADAR TECHNOLOGIES, Proceedings of the ХIХ International Forum on the problems of science, technology and education, p. 76-78, (2015) (in Russian).
[10]	E. N. Terentiev, N. E. Terentyev MATHEMATICAL PRINCIPLES OF SETTING MEASURING-COMPUTING SYSTEMS AND REGULARIZATION, NOTES OF THE RAS, PHYSICAL SERIES, 2015, Volume 79, No. 12, p. 1633-1637 (in Russian).
[11]	I Terentiev, E. N. and Terentiev, N. E. //ISSN 1062-8738, Bulletin of the Russian Academy of Science. Physics, 2015, Vol. 79, No 12, pp. 1427-1431, DOI 10.3103/S1062873815120229.
[12]	E. N. Terentyev, N. E. Terentyev, Yu. A. Pirogov, I. I. Farshakova, Physical Principles for Setting Apparatus Functions of Measuring Instruments, SCIENTIFIC NOTES OF THE PHYSICAL FACULTY OF MOSCOW UNIVERSITY, 9 pp., No. 6, 1761005 (2017) (in Russian).
[13]	E. N. Terentyev, N. E. Shilin-Terentyev Conditional super-resolution with classifiers, SCIENTIFIC NOTES OF THE PHYSICAL FACULTY OF THE MOSCOW UNIVERSITY, No. 5 1850306, p. 1-9 (2018) (in Russian).
[14]	Terentiev E. N., Terentiev N. E., Farshakova I. I., PMMEEP 2017, Physical and Mathematical Modeling of Earth and Environment Processes, 19 Chapter, Principles of Controlling the Apparatus Function for Achieving Super-Resolution in images, pp. 171-182, Number of pages 382, Springer International Publishing, DOI: 10.1007/978-3-319-77788-7_19C.
[15]	E. N. Terentiev, N. E. Shilin-Terentiev, Physical and Mathematical Modeling of Earth and Environment Processes (2018), Classifiers in Super-Resolution Problems, pp. 441-455, Springer Proceedings in Earth and Environmental Sciences. Springer, Cham, doi.org/10.1007/978-3-030-11533-3_44.
[16]	The Event Horizon Telescope Collaboration, First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, The Astrophysical Journal Letters, 875: L1 (17pp), 2019 April 10, https://doi.org/10.3847/2041-8213/ab0ec7.

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Evgeni Nikolaevich Terentiev, Irina Igorevna Farshakova, Nikolay Evgenyevich Shilin-Terentyev. (2019). Apodization of Black Holes in Super-Resolution Problems. American Journal of Astronomy and Astrophysics, 7(3), 39-47. https://doi.org/10.11648/j.ajaa.20190703.11

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ACS Style

Evgeni Nikolaevich Terentiev; Irina Igorevna Farshakova; Nikolay Evgenyevich Shilin-Terentyev. Apodization of Black Holes in Super-Resolution Problems. Am. J. Astron. Astrophys. 2019, 7(3), 39-47. doi: 10.11648/j.ajaa.20190703.11

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AMA Style

Evgeni Nikolaevich Terentiev, Irina Igorevna Farshakova, Nikolay Evgenyevich Shilin-Terentyev. Apodization of Black Holes in Super-Resolution Problems. Am J Astron Astrophys. 2019;7(3):39-47. doi: 10.11648/j.ajaa.20190703.11

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@article{10.11648/j.ajaa.20190703.11,
  author = {Evgeni Nikolaevich Terentiev and Irina Igorevna Farshakova and Nikolay Evgenyevich Shilin-Terentyev},
  title = {Apodization of Black Holes in Super-Resolution Problems},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {7},
  number = {3},
  pages = {39-47},
  doi = {10.11648/j.ajaa.20190703.11},
  url = {https://doi.org/10.11648/j.ajaa.20190703.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20190703.11},
  abstract = {Methods for identifying hidden objects are usually associated with the term apodization. The problem definitions of super-resolution must begin with the choice of the corresponding hidden object — the working discrete model of Apparatus Function (AF). With apodization such Black Holes, we will associate the mathematical invers problem of choosing working AFs with reversible R=O-1 and a small inverse norm Nor (R)=||R||. The apodization setting of super-resolution tasks, the indication of objects arise in the analysis of the Characteristics of Circumstances (CC) of the O AF models. The article provides examples of demonstration of CС with the choice of a discrete model of AF O with the usual inversions R=O-1 and without using a priori information about the type of solutions, as is customary in the regularization method [1]. The latter circumstance allowed us to solve the actual problem of the Super-Resolution of the image of the Black Hole Powehi shadow on low-accuracy data [16].},
 year = {2019}
}

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TY  - JOUR
T1  - Apodization of Black Holes in Super-Resolution Problems
AU  - Evgeni Nikolaevich Terentiev
AU  - Irina Igorevna Farshakova
AU  - Nikolay Evgenyevich Shilin-Terentyev
Y1  - 2019/10/20
PY  - 2019
N1  - https://doi.org/10.11648/j.ajaa.20190703.11
DO  - 10.11648/j.ajaa.20190703.11
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
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EP  - 47
PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.ajaa.20190703.11
AB  - Methods for identifying hidden objects are usually associated with the term apodization. The problem definitions of super-resolution must begin with the choice of the corresponding hidden object — the working discrete model of Apparatus Function (AF). With apodization such Black Holes, we will associate the mathematical invers problem of choosing working AFs with reversible R=O-1 and a small inverse norm Nor (R)=||R||. The apodization setting of super-resolution tasks, the indication of objects arise in the analysis of the Characteristics of Circumstances (CC) of the O AF models. The article provides examples of demonstration of CС with the choice of a discrete model of AF O with the usual inversions R=O-1 and without using a priori information about the type of solutions, as is customary in the regularization method [1]. The latter circumstance allowed us to solve the actual problem of the Super-Resolution of the image of the Black Hole Powehi shadow on low-accuracy data [16].
VL  - 7
IS  - 3
ER  -

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Author Information

Evgeni Nikolaevich Terentiev

M. V. Lomonosov Moscow State University, Faculty of Physics, Department Mathematical Modelling and Informatics, Moscow, Russia
Irina Igorevna Farshakova

M. V. Lomonosov Moscow State University, Faculty of Physics, Department Mathematical Modelling and Informatics, Moscow, Russia
Nikolay Evgenyevich Shilin-Terentyev

EPAM Systems, Moscow, Russia

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APA Style

Evgeni Nikolaevich Terentiev, Irina Igorevna Farshakova, Nikolay Evgenyevich Shilin-Terentyev. (2019). Apodization of Black Holes in Super-Resolution Problems. American Journal of Astronomy and Astrophysics, 7(3), 39-47. https://doi.org/10.11648/j.ajaa.20190703.11

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ACS Style

Evgeni Nikolaevich Terentiev; Irina Igorevna Farshakova; Nikolay Evgenyevich Shilin-Terentyev. Apodization of Black Holes in Super-Resolution Problems. Am. J. Astron. Astrophys. 2019, 7(3), 39-47. doi: 10.11648/j.ajaa.20190703.11

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AMA Style

Evgeni Nikolaevich Terentiev, Irina Igorevna Farshakova, Nikolay Evgenyevich Shilin-Terentyev. Apodization of Black Holes in Super-Resolution Problems. Am J Astron Astrophys. 2019;7(3):39-47. doi: 10.11648/j.ajaa.20190703.11

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@article{10.11648/j.ajaa.20190703.11,
  author = {Evgeni Nikolaevich Terentiev and Irina Igorevna Farshakova and Nikolay Evgenyevich Shilin-Terentyev},
  title = {Apodization of Black Holes in Super-Resolution Problems},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {7},
  number = {3},
  pages = {39-47},
  doi = {10.11648/j.ajaa.20190703.11},
  url = {https://doi.org/10.11648/j.ajaa.20190703.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20190703.11},
  abstract = {Methods for identifying hidden objects are usually associated with the term apodization. The problem definitions of super-resolution must begin with the choice of the corresponding hidden object — the working discrete model of Apparatus Function (AF). With apodization such Black Holes, we will associate the mathematical invers problem of choosing working AFs with reversible R=O-1 and a small inverse norm Nor (R)=||R||. The apodization setting of super-resolution tasks, the indication of objects arise in the analysis of the Characteristics of Circumstances (CC) of the O AF models. The article provides examples of demonstration of CС with the choice of a discrete model of AF O with the usual inversions R=O-1 and without using a priori information about the type of solutions, as is customary in the regularization method [1]. The latter circumstance allowed us to solve the actual problem of the Super-Resolution of the image of the Black Hole Powehi shadow on low-accuracy data [16].},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Apodization of Black Holes in Super-Resolution Problems
AU  - Evgeni Nikolaevich Terentiev
AU  - Irina Igorevna Farshakova
AU  - Nikolay Evgenyevich Shilin-Terentyev
Y1  - 2019/10/20
PY  - 2019
N1  - https://doi.org/10.11648/j.ajaa.20190703.11
DO  - 10.11648/j.ajaa.20190703.11
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 39
EP  - 47
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20190703.11
AB  - Methods for identifying hidden objects are usually associated with the term apodization. The problem definitions of super-resolution must begin with the choice of the corresponding hidden object — the working discrete model of Apparatus Function (AF). With apodization such Black Holes, we will associate the mathematical invers problem of choosing working AFs with reversible R=O-1 and a small inverse norm Nor (R)=||R||. The apodization setting of super-resolution tasks, the indication of objects arise in the analysis of the Characteristics of Circumstances (CC) of the O AF models. The article provides examples of demonstration of CС with the choice of a discrete model of AF O with the usual inversions R=O-1 and without using a priori information about the type of solutions, as is customary in the regularization method [1]. The latter circumstance allowed us to solve the actual problem of the Super-Resolution of the image of the Black Hole Powehi shadow on low-accuracy data [16].
VL  - 7
IS  - 3
ER  -

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