Results 11 to 20 of about 541,360 (283)
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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Parameter selection for total-variation-based image restoration using discrepancy principle [PDF]
IEEE Transactions on Image Processing, 2012 There are two key issues in successfully solving the image restoration problem: 1) estimation of the regularization parameter that balances data fidelity with the regularity of the solution and 2) development of efficient numerical techniques for computing the solution.
You-Wei, Wen, Raymond H, Chan
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ON MOROZOV’S DISCREPANCY PRINCIPLE FOR NONLINEAR ILL-POSED EQUATIONS [PDF]
Bulletin of the Australian Mathematical Society, 2009 AbstractMorozov’s discrepancy principle is one of the simplest and most widely used parameter choice strategies in the context of regularization of ill-posed operator equations. Although many authors have considered this principle under general source conditions for linear ill-posed problems, such study for nonlinear problems is restricted to only a ...
M Thamban Nair
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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.
Mathé, Peter, Pereverzev, Sergei V.
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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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Implicit iteration methods in Hilbert scales under general smoothness conditions [PDF]
, 2010 For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales.
Jin, Qinian, Tautenhahn, Ulrich
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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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Morozov's Discrepancy Principle under General Source Conditions
Zeitschrift für Analysis und ihre Anwendungen, 2003 In this paper we study linear ill-posed problems Ax = y in a Hilbert space setting where instead of exact data y noisy data y^\delta are given satisfying
Nair, M. Thamban +2 more
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Discrepancy Sets for Combined Least Squares Projection and Tikhonov Regularization
Mathematical Modelling and Analysis, 2017 To solve a linear ill-posed problem, a combination of the finite dimensional least squares projection method and the Tikhonov regularization is considered. The dimension of the projection is treated as the second parameter of regularization.
Teresa Reginska
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Mathematical Modelling and Analysis, 2014 In this paper we consider the problem for identifying an unknown steady source in a space fractional diffusion equation. A truncation method based on a Hermite function expansion is proposed, and the regularization parameter is chosen by a discrepancy ...
Zhenyu Zhao +3 more
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