Results 11 to 20 of about 2,897 (246)
Nearly Exact Discrepancy Principle for Low-Count Poisson Image Restoration [PDF]
Journal of Imaging, 2021 The effectiveness of variational methods for restoring images corrupted by Poisson noise strongly depends on the suitable selection of the regularization parameter balancing the effect of the regulation term(s) and the generalized Kullback–Liebler ...
Francesca Bevilacqua +3 more
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The discretized discrepancy principle under general source conditions
Journal of Complexity, 2006 For solving linear ill-posed operator equations in a Hilbert space the authors suggest a class of finite-dimensional regularization methods that use a discrete discrepancy principle of a posteriori parameter choice. Relations to other parameter choice strategies are discussed.
Peter Mathé, Sergei V Pereverzev
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Mathematics, 2020 This paper deals with the Tikhonov regularization for nonlinear ill-posed operator equations in Hilbert scales with oversmoothing penalties. One focus is on the application of the discrepancy principle for choosing the regularization parameter and its ...
Bernd Hofmann, Hofmann Bernd
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On the discrepancy principle for stochastic gradient descent [PDF]
Inverse Problems, 2020 Abstract Stochastic gradient descent (SGD) is a promising numerical method for solving large-scale inverse problems. However, its theoretical properties remain largely underexplored in the lens of classical regularization theory. In this note, we study the classical discrepancy principle, one of the most popular a posteriori choice rules,
Tim Jahn, Bangti Jin
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Journal of Mathematical Analysis and Applications, 2005 The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem approximately, rather than exactly, and in the proof of a stability result.
A G Ramm
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Analyzing the discrepancy principle for kernelized spectral filter learning algorithms
J. Mach. Learn. Res., 2020 68 pages, 4 ...
Celisse, Alain, Wahl, Martin
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An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 Recently, Tautenhahn and Hämarik (1999) have considered a monotone rule as a parameter choice strategy for choosing the regularization parameter while considering approximate solution of an ill-posed operator equation Tx=y, where T is a bounded linear ...
Santhosh George, M. Thamban Nair
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On saturation of the discrepancy principle for nonlinear Tikhonov regularization in Hilbert spaces
Applied Mathematics LettersIn this paper we revisit the discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems in Hilbert spaces and provide some new and improved saturation results under less restrictive conditions, comparing with the existing results in the literature.
Qinian Jin
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On the discrepancy principle and generalised maximum likelihood for regularisation [PDF]
Bulletin of the Australian Mathematical Society, 1995 Let fnλ be the regularised solution of a general, linear operator equation, K f0 = g, from discrete, noisy data yi = g(xi ) + εi, i = 1, …, n, where εi are uncorrelated random errors with variance σ2. In this paper, we consider the two well–known methods – the discrepancy principle and generalised maximum likelihood (GML), for choosing the crucial ...
Lukas, M.A.
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, 2012 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. It is crucial to choose the parameter appropriately. Here, a variant of the discrepancy principle is analyzed.
Anzengruber, Stephan W. +2 more
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