Signal Processing System Mathematical Microscope

Evgeni Nikolaevich Terentiev; Irina Igorevna Farshakova; Irina Nikolaevna Prikhodko; Nikolay Evgenievich Shilin-Terentyev

doi:doi:10.11648/j.sjams.20190705.12

Signal Processing System Mathematical Microscope

Evgeni Nikolaevich Terentiev, Irina Igorevna Farshakova, Irina Nikolaevna Prikhodko, Nikolay Evgenievich Shilin-Terentyev

Published in Science Journal of Applied Mathematics and Statistics (Volume 7, Issue 5)

Received: 26 June 2019 Accepted: 31 July 2019 Published: 15 October 2019

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Abstract

Conditionality is the main setting of Apparatus Function (AF) O to increase resolution. The conditionality is numerically equal to the reciprocal of the minimum value of Modulation Transfer Function (MTF) |M (O)| or the magnitude of this gap. We introduce the magnitude SR of the estimating super-resolution. The concept of a Mathematical Microscope (MM) is formulated in this paper.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 7, Issue 5)
DOI	10.11648/j.sjams.20190705.12
Page(s)	71-78
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

Super-Resolution, Conditionality, Apodization in Inevertability, Modulation Transfer Function, Convolution, Fourier Transform

References

[1]	Tikhonov, A. N., Ufimtsev, M. V., Statistical processing of experimental results, Publishing house of Moscow University (1988) (in Russian).
[2]	Yuri A. Pirogov, M. V. Lomonosov Moscow State Univ. (Russia); Magdy F. Attia, Johnson C. Smith Univ. (United States); Valeri V. Gladun, Andrey I. Dubina, Dmitri A. Tischenko, Evgeni N. Terentiev, M. V. Lomonosov Moscow State Univ. (Russia), Superresolution in millimeter-wave imaging technology, published in Proceedings Volume 3064: Passive Millimeter-Wave Imaging Technology, June 1997, Available on the SPIE Digital Library.
[3]	Yuri A. Pirogov, M. V. Lomonosov Moscow State Univ. (Russia); Magdy F. Attia, Johnson C. Smith Univ. (United States); Isaiah M. Blankson, NASA Aerospace Research Div. (United States); Valeri V. Gladun, M. V. Lomonosov Moscow State Univ. (Russia); C. D. Papanicolopoulos, Georgia Tech Research Institute (United States); Dmitri A. Tishchenko, Evgeni N. Terentiev, Oksana A. Tarasova, M. V. Lomonosov Moscow State Univ. (Russia). Optimization of radiovision systems in millimeter-wave range, published in Proceedings Volume 3378: Passive Millimeter-Wave Imaging Technology II, August 1998, Available on the SPIE Digital Library.
[4]	Yuri A. Pirogov, Valeri V. Gladun, Evgeni N. Terentiev, Dmitri A. Tischenko, Cheon W. Cho, Vladimir S. Ivanov, Moscow State Univ. (Russia), 3-mm wave range passive radio imaging system of high resolution, published in Proceedings Volume 4032: Passive Millimeter-Wave Imaging Technology IV, July 2000, Available on the SPIE Digital Library.
[5]	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), Ultraresolution of microwave, color, and synthetic color images, published in Proceedings Volume 5573: Image and Signal Processing for Remote Sensing X, November 2004, Available on the SPIE Digital Library.
[6]	Evgeni N. Terentiev, Nikolay E. Terentiev, M. V. Lomonosov Moscow State Univ. (Russia), Applications of pointed ultra-resolution method in microwave imaging, published in Proceedings Volume 5789: Passive Millimeter-Wave Imaging Technology VIII, May 2005, Available on the SPIE Digital Library.
[7]	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.
[8]	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).
[9]	Terentyev E. N., Terentyev N. E. PROBLEMS OF MULTI-BEAMS MEASURING - COMPUTING SYSTEMS, Proceedings of the ХIХ International Forum on problems of science, technology and education, p. 94-95 (2015) (in Russian).
[10]	Terentiev E. N., Terentyev N. E. ADEQUATE SETTINGS OF A LOT OF BEAM COMB IN RADAR TECHNOLOGIES, Proceedings of the ХIХ International Forum on the problems of science, technology and education, p. 76-78, (2015) (in Russian).
[11]	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).
[12]	Terentiev, E. N., Terentiev, N. E.: Bulletin of the Russian Academy of Science. Physics, vol. 79, No 12, pp. 1427-1431 (2015) doi: 10.3103/S1062873815120229.
[13]	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).
[14]	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.
[15]	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.
[16]	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).

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APA Style

Evgeni Nikolaevich Terentiev, Irina Igorevna Farshakova, Irina Nikolaevna Prikhodko, Nikolay Evgenievich Shilin-Terentyev. (2019). Signal Processing System Mathematical Microscope. Science Journal of Applied Mathematics and Statistics, 7(5), 71-78. https://doi.org/10.11648/j.sjams.20190705.12

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ACS Style

Evgeni Nikolaevich Terentiev; Irina Igorevna Farshakova; Irina Nikolaevna Prikhodko; Nikolay Evgenievich Shilin-Terentyev. Signal Processing System Mathematical Microscope. Sci. J. Appl. Math. Stat. 2019, 7(5), 71-78. doi: 10.11648/j.sjams.20190705.12

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AMA Style

Evgeni Nikolaevich Terentiev, Irina Igorevna Farshakova, Irina Nikolaevna Prikhodko, Nikolay Evgenievich Shilin-Terentyev. Signal Processing System Mathematical Microscope. Sci J Appl Math Stat. 2019;7(5):71-78. doi: 10.11648/j.sjams.20190705.12

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@article{10.11648/j.sjams.20190705.12,
  author = {Evgeni Nikolaevich Terentiev and Irina Igorevna Farshakova and Irina Nikolaevna Prikhodko and Nikolay Evgenievich Shilin-Terentyev},
  title = {Signal Processing System Mathematical Microscope},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {7},
  number = {5},
  pages = {71-78},
  doi = {10.11648/j.sjams.20190705.12},
  url = {https://doi.org/10.11648/j.sjams.20190705.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20190705.12},
  abstract = {Conditionality is the main setting of Apparatus Function (AF) O to increase resolution. The conditionality is numerically equal to the reciprocal of the minimum value of Modulation Transfer Function (MTF) |M (O)| or the magnitude of this gap. We introduce the magnitude SR of the estimating super-resolution. The concept of a Mathematical Microscope (MM) is formulated in this paper.},
 year = {2019}
}

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TY  - JOUR
T1  - Signal Processing System Mathematical Microscope
AU  - Evgeni Nikolaevich Terentiev
AU  - Irina Igorevna Farshakova
AU  - Irina Nikolaevna Prikhodko
AU  - Nikolay Evgenievich Shilin-Terentyev
Y1  - 2019/10/15
PY  - 2019
N1  - https://doi.org/10.11648/j.sjams.20190705.12
DO  - 10.11648/j.sjams.20190705.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 71
EP  - 78
PB  - Science Publishing Group
SN  - 2376-9513
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AB  - Conditionality is the main setting of Apparatus Function (AF) O to increase resolution. The conditionality is numerically equal to the reciprocal of the minimum value of Modulation Transfer Function (MTF) |M (O)| or the magnitude of this gap. We introduce the magnitude SR of the estimating super-resolution. The concept of a Mathematical Microscope (MM) is formulated in this paper.
VL  - 7
IS  - 5
ER  -

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Author Information

Evgeni Nikolaevich Terentiev

M. V. Lomonosov Moscow State University, Faculty of Physics, Moscow, Russia
Irina Igorevna Farshakova

M. V. Lomonosov Moscow State University, Faculty of Physics, Moscow, Russia
Irina Nikolaevna Prikhodko

M. V. Lomonosov Moscow State University, Faculty of Physics, Moscow, Russia
Nikolay Evgenievich Shilin-Terentyev

EPAM Systems, Moscow, Russia

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Plain Text BibTeX RIS

APA Style

Evgeni Nikolaevich Terentiev, Irina Igorevna Farshakova, Irina Nikolaevna Prikhodko, Nikolay Evgenievich Shilin-Terentyev. (2019). Signal Processing System Mathematical Microscope. Science Journal of Applied Mathematics and Statistics, 7(5), 71-78. https://doi.org/10.11648/j.sjams.20190705.12

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ACS Style

Evgeni Nikolaevich Terentiev; Irina Igorevna Farshakova; Irina Nikolaevna Prikhodko; Nikolay Evgenievich Shilin-Terentyev. Signal Processing System Mathematical Microscope. Sci. J. Appl. Math. Stat. 2019, 7(5), 71-78. doi: 10.11648/j.sjams.20190705.12

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AMA Style

Evgeni Nikolaevich Terentiev, Irina Igorevna Farshakova, Irina Nikolaevna Prikhodko, Nikolay Evgenievich Shilin-Terentyev. Signal Processing System Mathematical Microscope. Sci J Appl Math Stat. 2019;7(5):71-78. doi: 10.11648/j.sjams.20190705.12

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@article{10.11648/j.sjams.20190705.12,
  author = {Evgeni Nikolaevich Terentiev and Irina Igorevna Farshakova and Irina Nikolaevna Prikhodko and Nikolay Evgenievich Shilin-Terentyev},
  title = {Signal Processing System Mathematical Microscope},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {7},
  number = {5},
  pages = {71-78},
  doi = {10.11648/j.sjams.20190705.12},
  url = {https://doi.org/10.11648/j.sjams.20190705.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20190705.12},
  abstract = {Conditionality is the main setting of Apparatus Function (AF) O to increase resolution. The conditionality is numerically equal to the reciprocal of the minimum value of Modulation Transfer Function (MTF) |M (O)| or the magnitude of this gap. We introduce the magnitude SR of the estimating super-resolution. The concept of a Mathematical Microscope (MM) is formulated in this paper.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Signal Processing System Mathematical Microscope
AU  - Evgeni Nikolaevich Terentiev
AU  - Irina Igorevna Farshakova
AU  - Irina Nikolaevna Prikhodko
AU  - Nikolay Evgenievich Shilin-Terentyev
Y1  - 2019/10/15
PY  - 2019
N1  - https://doi.org/10.11648/j.sjams.20190705.12
DO  - 10.11648/j.sjams.20190705.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 71
EP  - 78
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20190705.12
AB  - Conditionality is the main setting of Apparatus Function (AF) O to increase resolution. The conditionality is numerically equal to the reciprocal of the minimum value of Modulation Transfer Function (MTF) |M (O)| or the magnitude of this gap. We introduce the magnitude SR of the estimating super-resolution. The concept of a Mathematical Microscope (MM) is formulated in this paper.
VL  - 7
IS  - 5
ER  -

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