28 citations · 59 across the 10 of their papers we have counts for
12 papers
Duality of uncomplemented null-space and non-closed range and its impact on the regularization of Mazur-type operators
Jens Flemming, Bernd Hofmann
Up to now operators with uncomplemented null-space have been playing only a minor role in regularization theory for ill-posed inverse problems in Banach spaces. We show that ill-po…
A note on the Goldberg-Thorp example in light of the classification of linear ill-posed problems in Banach spaces
Bernd Hofmann, Jens Flemming
This note considers the strictly singular mapping, denoted by , from onto of an example by Goldberg and Thorp from 1963 as a typical hybrid-type operator in th…
New aspects of ill-posedness classification in Banach spaces
Jens Flemming, Bernd Hofmann
Motivated by a seminal paper of professor M. Z. Nashed published in 1987 on classification of ill-posed linear operator equations and distinguishing two types of ill-posedness in B…
A simple linear time algorithm for smallest enclosing circles on the (hemi)sphere
Jens Flemming
Based on Welzl's algorithm for smallest circles and spheres we develop a simple linear time algorithm for finding the smallest circle enclosing a point cloud on a sphere. The algor…
A converse result for Banach space convergence rates in Tikhonov-type convex regularization of ill-posed linear equations
Jens Flemming
We consider Tikhonov-type variational regularization of ill-posed linear operator equations in Banach spaces with general convex penalty functionals. Upper bounds for certain error…
There always is a variational source condition for nonlinear problems in Banach spaces
Jens Flemming
Variational source conditions proved useful for deriving convergence rates for Tikhonov's regularization method and also for other methods. Up to now such conditions have been veri…
Injectivity and weak*-to-weak continuity suffice for convergence rates in -regularization
Jens Flemming, Daniel Gerth
We show that the convergence rate of -regularization for linear ill-posed equations is always if the exact solution is sparse and if the considered operator is injec…
A unified approach to convergence rates for -regularization and lacking sparsity
Jens Flemming, Bernd Hofmann, Ivan Veselic
In -regularization, which is an important tool in signal and image processing, one usually is concerned with signals and images having a sparse representation in some suita…
On -regularization in light of Nashed's ill-posedness concept
Jens Flemming, Bernd Hofmann, Ivan Veselic
Based on the powerful tool of variational inequalities, in recent papers convergence rates results on -regularization for ill-posed inverse problems have been formulated in…
Convergence rates in -regularization when the basis is not smooth enough
Jens Flemming, Markus Hegland
Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumpt…
Convergence rates in -regularization if the sparsity assumption fails
Martin Burger, Jens Flemming, Bernd Hofmann
Variational sparsity regularization based on -norms and other nonlinear functionals has gained enormous attention recently, both with respect to its applications and its ma…
A new approach to source conditions in regularization with general residual term
Jens Geissler, Bernd Hofmann
This paper addresses Tikhonov like regularization methods with convex penalty functionals for solving nonlinear ill-posed operator equations formulated in Banach or, more general,…