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Uspekhi Fizicheskikh Nauk, 1995, Volume 165, Number 2, Pages 143–176
DOI: https://doi.org/10.3367/UFNr.0165.199502b.0143
(Mi ufn1051)
 

This article is cited in 29 scientific papers (total in 29 papers)

REVIEWS OF TOPICAL PROBLEMS

Image restoration with minimum a priori information

V. Yu. Terebizh

Crimean Laboratory of Shternberg Astronomical Institute, Moscow State University, Nauchnii
Abstract: A consistent approach to the image restoration problem is presented, wich does not use Bayesian a priori information. Photon noise is taken into account. The unknown object is treated as a multidimensional set of parameters that have to be statistically estimated in an efficient way. The approach is based on an extended notion of feasible estimate (in the sense of information theory) and on Occam's razor rule of choosing the simplest object which is consistent with the data. Occam's rule is applied by transformation to principal components of the inverse (or maximum likelihood) estimate, which are generated by Fisher's information matrix. The same approach can also be applied to various other inverse problems.
Received: January 1, 1995
English version:
Physics–Uspekhi, 1995, Volume 38, Issue 2, Pages 137–167
DOI: https://doi.org/10.1070/PU1995v038n02ABEH000068
Bibliographic databases:
Document Type: Article
PACS: 95.75.-z, 95.75.Pq
Language: Russian


Citation: V. Yu. Terebizh, “Image restoration with minimum a priori information”, UFN, 165:2 (1995), 143–176; Phys. Usp., 38:2 (1995), 137–167
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  • https://www.mathnet.ru/eng/ufn1051
  • https://www.mathnet.ru/eng/ufn/v165/i2/p143
  • This publication is cited in the following 29 articles:
    1. Yu. P. Pyt'ev, A. I. Chulichkov, O. V. Falomkina, D. A. Balakin, “Data Analysis and Interpretation: Methods of Computer-Aided Measuring Transducer Theory, Morphological Analysis, Possibility Theory, and Subjective Mathematical Modeling”, Pattern Recognit. Image Anal., 33:4 (2023), 1515  crossref
    2. Gytis Kulaitis, Axel Munk, Frank Werner, “What is resolution? A statistical minimax testing perspective on superresolution microscopy”, Ann. Statist., 49:4 (2021)  crossref
    3. Aleksandr Yakovlevich Kalyuzhnyi, “Metod glavnykh informativnykh komponent v zadachakh statisticheskikh izmerenii parametrov signalov (sistematizirovannyi obzor)”, Izvestiya vuzov. Radioelektronika, 62:11 (2019), 643  crossref
    4. O. Y. Kaliuzhnyi, “Method of Principal Informative Components in Problems of Statistical Measurements of Signal Parameters (Systematic Review)”, Radioelectron.Commun.Syst., 62:11 (2019), 541  crossref
    5. D. V. Kurlikovskii, A. L. Ageev, T. V. Antonova, “Issledovanie porogovogo (korrelyatsionnogo) metoda i ego prilozhenie k lokalizatsii osobennostei”, Sib. elektron. matem. izv., 13 (2016), 829–848  mathnet  crossref
    6. Alexeev A.K. Bondarev A.E., “on Important Information Dynamics”, Math. Montisnigri, 35 (2016), 68–79  isi
    7. A.V. Kozyrev, V.Yu. Kozhevnikov, M.S. Vorobyov, E.Kh. Baksht, A.G. Burachenko, “Reconstruction of electron beam energy spectra for vacuum and gas diodes”, Laser Part. Beams, 2015, 1  crossref
    8. A. V. Khovanskiy, “Fast variant of K-method with universal adjustable scheme of scanning for problems of view of sight tomography on tokamaks”, Math. Models Comput. Simul., 6:1 (2014), 80–91  mathnet  crossref  mathscinet
    9. A. L. Ageev, T. V. Antonova, “O nekorrektno postavlennykh zadachakh lokalizatsii osobennostei”, Tr. IMM UrO RAN, 17, no. 3, 2011, 30–45  mathnet  elib
    10. E H Baksht, A G Burachenko, V Yu Kozhevnikov, A V Kozyrev, I D Kostyrya, V F Tarasenko, “Spectrum of fast electrons in a subnanosecond breakdown of air-filled diodes at atmospheric pressure”, J Phys D Appl Phys, 43:30 (2010), 305201  crossref  isi  elib
    11. V. Yu. Terebizh, “Stochastic models in classical and quantum mechanics”, Bull Crim Astrophys Observ, 106:1 (2010), 103  crossref  adsnasa
    12. Yu. P. Pyt'ev, “Measurement-computation converter as a measurement facility”, Autom. Remote Control, 71:2 (2010), 303–319  mathnet  crossref  mathscinet  zmath  isi
    13. E. H Baksht, I. D. Kostyrya, V. F. Tarasenko, A. G. Burachenko, V. Yu. Kozhevnikov, A. V. Kozyrev, 2010 IEEE International Power Modulator and High Voltage Conference, 2010, 405  crossref
    14. I. S. Savanov, “Analysis of MOST light curves of the active stars ɛ Eri AND κ Cet”, Astron Rep, 53:10 (2009), 950  crossref  adsnasa  isi  elib
    15. A. A. Egorov, “Inverse problem of scattering of monochromatic light in a statistically irregular waveguide: Theory and numerical simulation”, Opt Spectrosc, 103:4 (2007), 621  crossref  adsnasa  isi  elib
    16. I. S. Savanov, K. G. Strassmeier, “Surface imaging with atomic and molecular features”, A&A, 444:3 (2005), 931  crossref
    17. A. V. Khovanskii, N. M. Vakhanelova, A. M. Demkin, L. N. Starodubtseva, M. A. Charikov, A. V. Shulzhenko, “Metody ultramalorakursnoi tomografii v diagnostike plazmy”, Matem. modelirovanie, 16:2 (2004), 111–117  mathnet  zmath
    18. E. A. Koptelova, E. V. Shimanovskaya, B. P. Artamonov, M. V. Sazhin, A. G. Yagola, “Two-stage algorithm for reconstructing the images of the gravitational lens QSO 2237+0305”, Astron Rep, 48:10 (2004), 826  crossref  adsnasa  isi
    19. V. Yu. Terebizh, “Quasi-optimal filtering in inverse problems”, Astronomical & Astrophysical Transactions, 23:2 (2004), 85  crossref
    20. I Rodionov, A Rodionov, I Shilov, “Imaging with MCP in molecular beam experiments”, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 471:1-2 (2001), 239  crossref  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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