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...

Full description

Saved in:
Bibliographic Details
Published inInstruments and experimental techniques (New York) Vol. 63; no. 5; pp. 657 - 668
Main Author Novikov-Borodin, A. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.11.2020
Springer Nature B.V
Subjects
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
Online AccessGet full text

Cover

More Information
Summary:— 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.
ISSN:0020-4412
1608-3180
DOI:10.1134/S0020441220050322