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Non‐stationary iterated Tikhonov–Morozov method and third‐order differential equations for the evaluation of unbounded operators
Author(s) -
Groetsch C. W.,
Scherzer O.
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/1099-1476(200010)23:15<1287::aid-mma165>3.0.co;2-n
Subject(s) - tikhonov regularization , mathematics , iterated function , differential equation , regularization (linguistics) , iterative method , mathematical analysis , differential operator , partial differential equation , algorithm , inverse problem , computer science , artificial intelligence
In this paper we analyse the non‐stationary iterative Tikhonov–Morozov method analytically and numerically for the stable evaluation of differential operators and for denoizing images. A relationship between non‐stationary iterative Tikhonov–Morozov regularization and a filtering technique based on a differential equation of third order is established and both methods are shown to be effective for denoizing images and for the stable evaluation of differential operators. The theoretical results are verified numerically on model problems in ultrasound imaging and numerical differentiation. Copyright © 2000 John Wiley & Sons, Ltd.