Direct Reconstruction of the Experimental Data in the Case of Ill-Conditioned Problems and in the Presence of Data Distortions
— The possibilities of reconstructing discrete experimental data using direct inversion, i.e., deconvolution, are investigated. Methods for optimization, smoothing, compensation, and decomposition are proposed, with which it is possible to reconstruct data with minimal information losses in many cas...
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| Published in | Instruments and experimental techniques (New York) Vol. 63; no. 5; pp. 657 - 668 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.11.2020
Springer Nature B.V |
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| Online Access | Get full text |
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| Abstract | —
The possibilities of reconstructing discrete experimental data using direct inversion, i.e., deconvolution, are investigated. Methods for optimization, smoothing, compensation, and decomposition are proposed, with which it is possible to reconstruct data with minimal information losses in many cases of ill-conditioned problems and in the presence of data distortions. These methods are based on the formation of well-conditioned systems with the compensation of accidental distortions from overdetermined systems of equations corresponding to the convolution equations using the linear transformations. A comparative analysis of the proposed methods is carried out. Their potentialities and accuracies of reconstruction are analyzed. Examples of the reconstruction are presented. |
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| AbstractList | Abstract—The possibilities of reconstructing discrete experimental data using direct inversion, i.e., deconvolution, are investigated. Methods for optimization, smoothing, compensation, and decomposition are proposed, with which it is possible to reconstruct data with minimal information losses in many cases of ill-conditioned problems and in the presence of data distortions. These methods are based on the formation of well-conditioned systems with the compensation of accidental distortions from overdetermined systems of equations corresponding to the convolution equations using the linear transformations. A comparative analysis of the proposed methods is carried out. Their potentialities and accuracies of reconstruction are analyzed. Examples of the reconstruction are presented. — The possibilities of reconstructing discrete experimental data using direct inversion, i.e., deconvolution, are investigated. Methods for optimization, smoothing, compensation, and decomposition are proposed, with which it is possible to reconstruct data with minimal information losses in many cases of ill-conditioned problems and in the presence of data distortions. These methods are based on the formation of well-conditioned systems with the compensation of accidental distortions from overdetermined systems of equations corresponding to the convolution equations using the linear transformations. A comparative analysis of the proposed methods is carried out. Their potentialities and accuracies of reconstruction are analyzed. Examples of the reconstruction are presented. |
| Author | Novikov-Borodin, A. V. |
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| Cites_doi | 10.1134/S0020441219040195 10.1134/S0020441218050226 10.1051/epjconf/202022603014 |
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| References | GonzalezR.Digital Image Processing2008 Novikov-Borodin, A.V., Preprint of Institute for Nuclear Research, Russian Academy of Sciences, Moscow, 2019, no. 1440/2019. OppenheimA.V.SchaferR.W.Discrete Time Signal Processing1989Englewood Cliffs, NJPrentice-Hall0676.42001 Novikov-Borodin, A.V., EPJ Web Conf., 2020, vol. 226, p. 03014. https://doi.org/10.1051/epjconf/202022603014 Vladimirov, V.S., Uravneniya matematicheskoi fiziki (Mathematical Physics Equations), Moscow: Nauka, 1981. MadisettiV.K.WilliamsD.B.Digital Signal Processing. Handbook1999LondonChapman and Hall Novikov-BorodinA.V.Instrum. Exp. Tech.20186178078710.1134/S0020441218050226 Novikov-BorodinA.V.Instrum. Exp. Tech.20196248048810.1134/S0020441219040195 Il’in, V.A. and Kim, G.D., Lineinaya algebra i analiticheskaya geometriya (Linear Algebra and Analytical Geometry), Moscow: Moscow State Univ., 1998. SmithS.W.The Scientist and Engineer’s Guide to Digital Signal Processing1999San Diego, CACalifornia Technical Publ. TikhonovA.N.ArseninV.Ya.Solutions of Ill-Posed Problems1977Washington, DCWinston and Sons0354.65028 Tikhonov, A.N. and Samarskii, A.A., Uravneniya matematicheskoi fiziki (Equations for Mathematical Physics), Moscow: Nauka, 1972. GolubD.H.Van LoanC.FMatrix Computations1989Baltimore, LondonJohn Hopkins Univ. Press0733.65016 JacksonL.B.Signals, Systems, and Transforms1991Reading, MAAddison-Wesley (8283_CR1) 1999 A.V. Novikov-Borodin (8283_CR8) 2018; 61 D.H. Golub (8283_CR12) 1989 8283_CR11 8283_CR10 8283_CR13 8283_CR14 L.B. Jackson (8283_CR5) 1991 A.V. Novikov-Borodin (8283_CR9) 2019; 62 A.V. Oppenheim (8283_CR4) 1989 R. Gonzalez (8283_CR7) 2008 A.N. Tikhonov (8283_CR2) 1977 S.W. Smith (8283_CR6) 1999 8283_CR3 |
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The possibilities of reconstructing discrete experimental data using direct inversion, i.e., deconvolution, are investigated. Methods for optimization,... Abstract—The possibilities of reconstructing discrete experimental data using direct inversion, i.e., deconvolution, are investigated. Methods for... |
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| SubjectTerms | Application of Computers in Experiments Compensation Convolution Distortion Electrical Engineering Ill-conditioned problems (mathematics) Linear transformations Mathematical analysis Measurement Science and Instrumentation Optimization Physical Chemistry Physics Physics and Astronomy Reconstruction |
| Title | Direct Reconstruction of the Experimental Data in the Case of Ill-Conditioned Problems and in the Presence of Data Distortions |
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