Zobrazeno 1 - 10
of 37
pro vyhledávání: '"Jahn, Tim"'
The fast computation of large kernel sums is a challenging task, which arises as a subproblem in any kernel method. We approach the problem by slicing, which relies on random projections to one-dimensional subspaces and fast Fourier summation. We pro
Externí odkaz:
http://arxiv.org/abs/2410.01316
Autor:
Jahn, Tim, Jin, Bangti
In recent years, new regularization methods based on (deep) neural networks have shown very promising empirical performance for the numerical solution of ill-posed problems, e.g., in medical imaging and imaging science. Due to the nonlinearity of neu
Externí odkaz:
http://arxiv.org/abs/2402.04610
Autor:
Griebel, Michael, Jahn, Tim
This paper discusses the error and cost aspects of ill-posed integral equations when given discrete noisy point evaluations on a fine grid. Standard solution methods usually employ discretization schemes that are directly induced by the measurement p
Externí odkaz:
http://arxiv.org/abs/2401.16250
Autor:
Jahn, Tim
In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian) noise is
Externí odkaz:
http://arxiv.org/abs/2207.05997
Autor:
Jahn, Tim
We consider linear inverse problems under white noise. These types of problems can be tackled with, e.g., iterative regularisation methods and the main challenge is to determine a suitable stopping index for the iteration. Convergence results for pop
Externí odkaz:
http://arxiv.org/abs/2204.14037
Autor:
Jahn, Tim
In this note we consider spectral cut-off estimators to solve a statistical linear inverse problem under arbitrary white noise. The truncation level is determined with a recently introduced adaptive method based on the classical discrepancy principle
Externí odkaz:
http://arxiv.org/abs/2202.12596
Autor:
Jahn, Tim
We consider a linear ill-posed equation in the Hilbert space setting under white noise. Known convergence results for the discrepancy principle are either restricted to Hilbert-Schmidt operators (and they require a self-similarity condition for the u
Externí odkaz:
http://arxiv.org/abs/2104.06184
Autor:
Jahn, Tim
We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the right hand
Externí odkaz:
http://arxiv.org/abs/2103.03545
Publikováno v:
IMA J. Numer. Anal. 43 (1), 443-500, 2023
We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right hand side is unknown and only accessible through discretised measurements corrupted by white noise with unknown arbitrary distribution. The me
Externí odkaz:
http://arxiv.org/abs/2010.04519
Autor:
Jahn, Tim, Jin, Bangti
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 cl
Externí odkaz:
http://arxiv.org/abs/2004.14625