Zobrazeno 1 - 10
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pro vyhledávání: '"Frikel, Jürgen"'
Inverse problems are inherently ill-posed and therefore require regularization techniques to achieve a stable solution. While traditional variational methods have well-established theoretical foundations, recent advances in machine learning based app
Externí odkaz:
http://arxiv.org/abs/2309.06573
In this article, we address the challenge of solving the ill-posed reconstruction problem in computed tomography using a translation invariant diagonal frame decomposition (TI-DFD). First, we review the concept of a TI-DFD for general linear operator
Externí odkaz:
http://arxiv.org/abs/2305.02708
In a number of tomographic applications, data cannot be fully acquired, resulting in a severely underdetermined image reconstruction. In such cases, conventional methods lead to reconstructions with significant artifacts. To overcome these artifacts,
Externí odkaz:
http://arxiv.org/abs/2304.11599
Solving inverse problems is central to a variety of important applications, such as biomedical image reconstruction and non-destructive testing. These problems are characterized by the sensitivity of direct solution methods with respect to data pertu
Externí odkaz:
http://arxiv.org/abs/2208.08500
In this paper, we consider the problem of feature reconstruction from incomplete x-ray CT data. Such problems occurs, e.g., as a result of dose reduction in the context medical imaging. Since image reconstruction from incomplete data is a severely il
Externí odkaz:
http://arxiv.org/abs/2202.10724
We present two methods that combine image reconstruction and edge detection in computed tomography (CT) scans. Our first method is as an extension of the prominent filtered backprojection algorithm. In our second method we employ $\ell^{1}$-regulariz
Externí odkaz:
http://arxiv.org/abs/2109.00428
Autor:
Göppel, Simon1 (AUTHOR), Frikel, Jürgen2 (AUTHOR) juergen.frikel@oth-regensburg.de, Haltmeier, Markus1 (AUTHOR) juergen.frikel@oth-regensburg.de
Publikováno v:
Mathematics (2227-7390). May2024, Vol. 12 Issue 10, p1606. 20p.
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and analyze the co
Externí odkaz:
http://arxiv.org/abs/2008.06219
We derive a new 3D model for magnetic particle imaging (MPI) that is able to incorporate realistic magnetic fields in the reconstruction process. In real MPI scanners, the generated magnetic fields have distortions that lead to deformed magnetic low-
Externí odkaz:
http://arxiv.org/abs/2004.13357
Autor:
Frikel, Jürgen, Haltmeier, Markus
We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame thresholdi
Externí odkaz:
http://arxiv.org/abs/1909.09364