Results 1 to 10 of about 1,273,558 (290)
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 [PDF]
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.
Sergei Pereverzev, Peter Mathé
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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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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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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, Christopher Hofmann
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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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Mathematics, 2021 We prove the logarithmic convergence rate of the families of usual and modified iterative Runge-Kutta methods for nonlinear ill-posed problems between Hilbert spaces under the logarithmic source condition, and numerically verify the obtained results. The
Pornsarp Pornsawad +2 more
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Open Mathematics, 2023 In this article, we investigate a spherically symmetric backward heat conduction problem, starting from the final temperature. This problem is severely ill posed: the solution (if it exists) does not depend continuously on the final data.
Cheng Wei, Liu Yi-Liang
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A modified Tikhonov regularization for unknown source in space fractional diffusion equation
Open Mathematics, 2022 In this article, we consider the identification of an unknown steady source in a class of fractional diffusion equations. A modified Tikhonov regularization method based on Hermite expansion is presented to deal with the ill-posedness of the problem.
Yu Kai, Gong Benxue, Zhao Zhenyu
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Open Mathematics, 2020 In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem.
Zhao Zhenyu, You Lei, Meng Zehong
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