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In this paper we provide a convergence analysis of some variational methods alternative to the classical Tikhonov regularization, namely Ivanov regularization (also called method of quasi solutions) with some versions of the discrepancy…
The Tikhonov-Phillips method is widely used for regularizing ill-posed inverse problems mainly due to the simplicity of its formulation as an optimization problem. The use of different penalizers in the functionals associated to the…
We present a new approach to convexification of the Tikhonov regularization using a continuation method strategy. We embed the original minimization problem into a one-parameter family of minimization problems. Both the penalty term and the…
In this paper, we consider the efficient numerical minimization of Tikhonov functionals resulting from total-variation (TV) regularization of linear inverse problems. Since the TV penalty is non-smooth, this is typically done either via…
Coherent techniques for searches of gravitational-wave bursts effectively combine data from several detectors, taking into account differences in their responses. The efforts are now focused on the maximum likelihood principle as the most…
We propose and analyze an iterative refinement of a modified Lavrentiev regularization method for deconvolution of the discrete Helmholtz-type differential filter. The modification for the Lavrentiev regularization method exploits the…
We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition…
Conditional stability estimates allow us to characterize the degree of ill-posedness of many inverse problems, but without further assumptions they are not sufficient for the stable solution in the presence of data perturbations. We here…
In this paper, we study the stochastic convergence of regularized solutions for backward heat conduction problems. These problems are recognized as ill-posed due to the exponential decay of eigenvalues associated with the forward problems.…
Several generalizations of the traditional Tikhonov-Phillips regularization method have been proposed during the last two decades. Many of these generalizations are based upon inducing stability throughout the use of different penalizers…
Many applications in science and engineering require the solution of large linear discrete ill-posed problems that are obtained by the discretization of a Fredholm integral equation of the first kind in several space-dimensions. The matrix…
This study investigates the iterative refinement method applied to the solution of linear discrete inverse problems by considering its application to the Tikhonov problem in mixed precision. Previous works on mixed precision iterative…
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…
We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account…
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…
In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…
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…
In this paper, we consider an inverse problem to determine a source term in a parabolic equation, where the data are obtained at a certain time. In general, this problem is ill-posed, therefore the Tikhonov regularization method is proposed…
In this paper we propose a new statistical stopping rule for constrained maximum likelihood iterative algorithms applied to ill-posed inverse problems. To this aim we extend the definition of Tikhonov regularization in a statistical…
Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…