180 citations · 1.2k across the 100 of their papers we have counts for
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Newton's methods for solving linear inverse problems with neural network coders
Otmar Scherzer, Bernd Hofmann, Zuhair Nashed
Neural networks functions are supposed to be able to encode the desired solution of an inverse problem very efficiently. In this paper, we consider the problem of solving linear in…
Singular Values of the Attenuated Photoacoustic Imaging Operator
Peter Elbau, Otmar Scherzer, Cong Shi
We analyse the ill-posedness of the photoacoustic imaging problem in the case of an attenuating medium. To this end, we introduce an attenuated photoacoustic operator and determine…
Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
Vinicius Albani, Peter Elbau, Maarten V. de Hoop +1
In this paper, we prove optimal convergence rates results for regularisation methods for solving linear ill-posed operator equations in Hilbert spaces. The result generalises exist…
Generalized Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
Roman Andreev, Peter Elbau, Maarten V. de Hoop +2
In recent years, a series of convergence rates conditions for regularization methods has been developed. Mainly, the motivations for developing novel conditions came from the desir…
Exact Solutions of One-Dimensional TGV
Christiane Pöschl, Otmar Scherzer
L2-TGV-regularization has been introduced by Bredies, Kunisch, and Pock. This regularization method requires careful tuning of two regularization parameters. The focus of this pape…
Local Analysis of Inverse Problems: Hölder Stability and Iterative Reconstruction
Maarten V. de Hoop, Lingyun Qiu, Otmar Scherzer
We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a…