Regularization Methods for Ill-Posed Problems

Jin Cheng and Bernd Hofmann
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Jin Cheng: Fudan University
Bernd Hofmann: Chemnitz University of Technology

Chapter 3 in Handbook of Mathematical Methods in Imaging, 2011, pp 87-109 from Springer

Abstract: Abstract In this chapter, we outline the mathematical theory of direct regularization methods for in general nonlinear and ill-posed inverse problems. One focus is on Tikhonov regularization in Hilbert spaces with quadratic misfit and penalty terms. Moreover, recent results of an extension of the theory to Banach spaces are presented concerning the variational regularization with convex penalty term. Five examples of parameter identification problems in integral and differential equations are given in order to show how to apply the theory of this chapter to specific inverse and ill-posed problems.

Keywords: Inverse Problem; Variational Inequality; Regularization Parameter; Penalty Term; Tikhonov Regularization (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-92920-0_3

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DOI: 10.1007/978-0-387-92920-0_3

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