Science Journal of Applied Mathematics and Statistics

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Signal Processing System Mathematical Microscope

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.

DOI 10.11648/j.sjams.20190705.12
Published in Science Journal of Applied Mathematics and Statistics (Volume 7, Issue 5, October 2019)
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), 2024. 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.
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Author Information
  • M. V. Lomonosov Moscow State University, Faculty of Physics, Moscow, Russia

  • M. V. Lomonosov Moscow State University, Faculty of Physics, Moscow, Russia

  • M. V. Lomonosov Moscow State University, Faculty of Physics, Moscow, Russia

  • EPAM Systems, Moscow, Russia

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    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://download.sciencepg.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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    T1  - Signal Processing System Mathematical Microscope
    AU  - Evgeni Nikolaevich Terentiev
    AU  - Irina Igorevna Farshakova
    AU  - Irina Nikolaevna Prikhodko
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    JO  - Science Journal of Applied Mathematics and Statistics
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    PB  - Science Publishing Group
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    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
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