Matrix approach to solution of the inverse problems for multimedia wireless communication links

Mikhail Sergeev, Nathan Blaunstein

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


The goal of this chapter is the analysis of a principal difference between the direct and inverse problems related to the applied electrodynamics, and radio, acoustic and optical wave physics, as well as, the relations of direct and inverse problems with each other. We use the concept of matrix or tensor equations technique for direct problem derivation, which deals with finding of the wave field for known distribution of sources of wave radiation. The same matrix approach is presented for the inverse problem resolving, which deals with determination and localization of the radiated sources’ distribution a few limited cases of canonical objects and media. The strict analytical solution of such problems is obtained only for special cases of sources distribution and signal reconstruction. New methodology of how to identify the shape, form, structure, and type of material and define the parameters of media via knowledge on the wave field spatial, temporal, and spectral distribution arrived at the wave receiver and recorded by the detector, localizing any source and eliminating image speeding, has been created.

Original languageEnglish
Title of host publicationIntelligent Systems Reference Library
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages20
StatePublished - 1 Jan 2020

Publication series

NameIntelligent Systems Reference Library
ISSN (Print)1868-4394
ISSN (Electronic)1868-4408


  • Direct problem
  • Hadamard principal
  • Inverse problem
  • Iteration algorithm
  • Least squares method
  • Levenberg–marquardt algorithm
  • Moore-Penrose matrix
  • Pseudo-inverse matrix singular-value decomposition
  • Singular regularization
  • Tikhonov’s approach

ASJC Scopus subject areas

  • General Computer Science
  • Information Systems and Management
  • Library and Information Sciences


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