Related papers: Projected Newton Method for noise constrained Tikh…
We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. In the…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
To solve convex optimization problems with a noisy gradient input, we analyze the global behavior of subgradient-like flows under stochastic errors. The objective function is composite, being equal to the sum of two convex functions, one…
Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, which are a necessity due to the ill-posedness of inverse problems. Tikhonov-type regularization methods are very popular in…
We study the application of Tikhonov regularization to ill-posed nonlinear operator equations. The objective of this work is to prove low order convergence rates for the discrepancy principle under low order source conditions of logarithmic…
We study the behaviour of Tikhonov regularisation on topological spaces with multiple regularisation terms. The main result of the paper shows that multi-parameter regularisation is well-posed in the sense that the results depend…
The $\chi^2$-principle generalizes the Morozov discrepancy principle (MDP) to the augmented residual of the Tikhonov regularized least squares problem. Weighting of the data fidelity by a known Gaussian noise distribution on the measured…
In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once…
This paper provides a new regularization method which is particularly suitable for linear exponentially ill-posed problems. Under logarithmic source conditions (which have a natural interpretation in terms of Sobolev spaces in the…
We study weighted Tikhonov regularization for large-scale linear discrete ill-posed problems with random noise. Under a polynomial upper-bound assumption on the generalized eigenvalues of the discrete forward operator, we derive stochastic…
This paper is concerned with the regularization of large-scale discrete inverse problems by means of inexact Krylov methods. Specifically, we derive two new inexact Krylov methods that can be efficiently applied to unregularized or…
Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method…
Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the…
From the viewpoint of inverse problem, the optimization of drug release based on the multi-laminated drug controlled release devices has been regarded as the solution problem of the diffusion equation initial value inverse problem. In view…
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…
Tikhonov regularization involves minimizing the combination of a data discrepancy term and a regularizing term, and is the standard approach for solving inverse problems. The use of non-convex regularizers, such as those defined by trained…
For approximately solving linear ill-posed problems in Hilbert spaces, we investigate the regularization properties of the aggregation method and the RatCG method. These recent algorithms use previously calculated solutions of Tikhonov…
We are concerned with structured $\ell_0$-norms regularization problems, with a twice continuously differentiable loss function and a box constraint. This class of problems have a wide range of applications in statistics, machine learning…
In this article we propose a novel nonstationary iterated Tikhonov (NIT) type method for obtaining stable approximate solutions to ill-posed operator equations modeled by linear operators acting between Hilbert spaces. Geometrical…
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. % By exploiting…