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On convergence rates for asymptotic discrepancy principle
Journal of Inverse and Ill-Posed Problems, 2016Abstract A series of recent numerical experiments for parameter estimation inverse problems in epidemiology [7, 6] have indicated that applicability of the discrepancy principle (DP) does not depend on the structure of a particular regularizing operator.
Alexandra Smirnova
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Applicable Analysis, 2014 The stable solution of ill-posed non-linear operator equations in Banach space requires regularization. One important approach is based on Tikhonov regularization, in which case a one-parameter family of regularized solutions is obtained.
Bernd Hofmann, Peter Mathé
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A discrepancy principle for Poisson data
Inverse Problems, 2010In applications of imaging science, such as emission tomography, fluorescence microscopy and optical/infrared astronomy, image intensity is measured via the counting of incident particles (photons, γ-rays, etc). Fluctuations in the emission-counting process can be described by modeling the data as realizations of Poisson random variables (Poisson data).
BERTERO, MARIO +4 more
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A modification of the generalized discrepancy principle
USSR Computational Mathematics and Mathematical Physics, 1983Translation from Zh. Vychisl. Mat. Mat. Fiz. 23, No.6, 1298-1303 (Russian) (1983; Zbl 0543.65033).
Kochikov, I. V. +2 more
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A generalized discrepancy principle for solving incompatible equations
USSR Computational Mathematics and Mathematical Physics, 1984Let \(Z\) be a reflexive Banach space with the property \(H\), \(D\) be a closed convex subset of \(Z\), \(0\in D\). Consider an incompatible equation \(Az=u\) in \(D\) (i.e. \(\mu =\inf \{\| Az-u\|: z\in D\}\ge 0)\) where \(A\) is a bounded linear operator from \(Z\) into a normed linear space \(U\), \(u\in U\), and suppose there is a normal ...
Kochikov, I. V. +2 more
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A generalized discrepancy principle for the L-pseudosolutions
USSR Computational Mathematics and Mathematical Physics, 1987See the review in Zbl 0638.47010.
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Principles of orthognathic management of dentofacial discrepancies
Dental Update, 2018Abstract: Individuals with severe dentofacial discrepancies that are beyond the scope of conventional orthodontic treatment will often require a joint orthodontic-surgical approach to manage their malocclusion. This treatment approach involving orthodontics in combination with orthognathic surgery is used to manage severe underlying skeletal ...
Kulraj S Achal +2 more
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Modular solvers for image restoration problems using the discrepancy principle
Numerical Linear Algebra with Applications, 2002AbstractMany problems in image restoration can be formulated as either an unconstrained non‐linear minimization problem, usually with aTikhonov‐like regularization, where the regularization parameter has to be determined; or as a fully constrained problem, where an estimate of the noise level, either the variance or the signal‐to‐noise ratio, is ...
Peter Blomgren, Tony F. Chan
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Comments on Morozov’s Discrepancy Principle
1983The choice of regularization parameter by Morozov’s principle is characterized in a new way and is related to another parameter choice strategy. An asymptotic order of accuracy is derived which is essentially best possible and a discrepancy principle is developed in a finite element context.
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