Results 1 to 10 of about 77,719 (148)
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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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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On the discrepancy principle for stochastic gradient descent
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, 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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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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Discrepancy principle for DSM II [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems
Mathematics, 2020 In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle.
Pornsarp Pornsawad +2 more
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On rules for stopping the conjugate gradient type methods in ill‐posed problems
Mathematical Modelling and Analysis, 2007 We consider stopping rules in conjugate gradient type iteration methods for solving linear ill‐posed problems with noisy data. The noise level may be known exactly or approximately or be unknown. We propose several new stopping rules, mostly for the case
Uno Hämarik, Reimo Palm
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