Inverse Problems with A Priori Information

Vladimir V. Vasin ()
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Vladimir V. Vasin: Institute of Mathematics and Mechanics UB RAS, Department of the ill-posed problems

Chapter Chapter 3 in Optimization and Regularization for Computational Inverse Problems and Applications, 2010, pp 35-64 from Springer

Abstract: Abstract For the last thirty years in the theory of ill-posed problems the direction of investigations was formed that joins with solving the ill-posed problems with a priori information. This is the class of problems, for which, together with the basic equation, additional information about the solution to be found is known, and this information is given in the form of some relations and restrictions that contains important data about the object under consideration. Inclusion of this information into algorithm plays the crucial role in increasing the accuracy of solution of the ill-posed (unstable) problem. It is especially important in the case when solution is not unique, since it allows one to select a solution that corresponds to reality. In this work, the review of methods for solving such problems is presented. Though the author touches all approaches known to him in this scope, the main attention is paid to the methodology that is developed by the Author and based on iterative processes of the Fejér type, which give flexible and effective realization for a wide class of a priori restrictions. In the final section, description of several applied inverse problems with the a priori information and numerical algorithms for their solving are given.

Keywords: Hilbert Space; Inverse Problem; Iterative Process; Strong Convergence; Tikhonov Regularization (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-13742-6_3

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DOI: 10.1007/978-3-642-13742-6_3

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