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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 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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Stochastic linear regularization methods: random discrepancy principle and applications
Inverse Problems, 2023Abstract The a posteriori stopping rule plays a significant role in the design of efficient stochastic algorithms for various tasks in computational mathematics, such as inverse problems, optimization, and machine learning. Through the lens of classical regularization theory, this paper describes a novel analysis of Morozov’s discrepancy
Ye Zhang, Chuchu Chen
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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.
Bakushinsky, Anatoly +1 more
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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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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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Heuristic discrepancy principle for variational regularization of inverse problems
Inverse Problems, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huan Liu +4 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 ...
Blomgren, Peter, Chan, Tony F.
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