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.
Citation:
V. Yu. Terebizh, “Image restoration with minimum a priori information”, UFN, 165:2 (1995), 143–176; Phys. Usp., 38:2 (1995), 137–167
Linking options:
https://www.mathnet.ru/eng/ufn1051
https://www.mathnet.ru/eng/ufn/v165/i2/p143
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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
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Alexeev A.K. Bondarev A.E., “on Important Information Dynamics”, Math. Montisnigri, 35 (2016), 68–79
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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
A. L. Ageev, T. V. Antonova, “O nekorrektno postavlennykh zadachakh lokalizatsii osobennostei”, Tr. IMM UrO RAN, 17, no. 3, 2011, 30–45
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
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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
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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
I. S. Savanov, K. G. Strassmeier, “Surface imaging with atomic and molecular features”, A&A, 444:3 (2005), 931
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
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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