Zobrazeno 1 - 10
of 57
pro vyhledávání: '"47A52, 65J20"'
Autor:
Mathé, Peter, Hofmann, Bernd
The difficulty for solving ill-posed linear operator equations in Hilbert space is reflected by the strength of ill-posedness of the governing operator, and the inherent solution smoothness. In this study we focus on the ill-posedness of the operator
Externí odkaz:
http://arxiv.org/abs/2410.17729
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on energy co
Externí odkaz:
http://arxiv.org/abs/2410.11467
Publikováno v:
Inverse Problems 40:015013 (2024)
Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of interest is not directly accessible but only after the inversion of a (po
Externí odkaz:
http://arxiv.org/abs/2212.12897
Publikováno v:
Applied Mathematics & Optimization, 88(2):51, 2023
We consider whether minimizers for total variation regularization of linear inverse problems belong to $L^\infty$ even if the measured data does not. We present a simple proof of boundedness of the minimizer for fixed regularization parameter, and de
Externí odkaz:
http://arxiv.org/abs/2203.03264
The Hausdorf moment problem (HMP) over the unit interval in an $L^2$-setting is a classical example of an ill-posed inverse problem. Since various applications can be rewritten in terms of the HMP, it has gathered significant attention in the literat
Externí odkaz:
http://arxiv.org/abs/2104.06029
We study the problem of regularization of inverse problems adopting a purely data driven approach, by using the similarity to the method of regularization by projection. We provide an application of a projection algorithm, utilized and applied in fra
Externí odkaz:
http://arxiv.org/abs/2103.05718
Publikováno v:
Inverse Problems 36 (2020) 125014
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and convex duali
Externí odkaz:
http://arxiv.org/abs/2005.14131
In this paper we propose a variational regularization method for denoising and inpainting of diffusion tensor magnetic resonance images. We consider these images as manifold-valued Sobolev functions, i.e. in an infinite dimensional setting, which are
Externí odkaz:
http://arxiv.org/abs/2004.01585
Autor:
Bao, Gang, Triki, Faouzi
The solution of a multi-frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived when the fr
Externí odkaz:
http://arxiv.org/abs/2002.09242
Autor:
Melching, Melanie, Scherzer, Otmar
We present a family of non-local variational regularization methods for solving tomographic problems, where the solutions are functions with range in a closed subset of the Euclidean space, for example if the solution only attains values in an embedd
Externí odkaz:
http://arxiv.org/abs/1911.06624