180 citations · 275 across the 19 of their papers we have counts for
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A square root velocity framework for curves of bounded variation
Markus Grasmair
The square root velocity transform is a powerful tool for the efficient computation of distances between curves. Also, after factoring out reparametrisations, it defines a distance…
Subgradient-based Lavrentiev regularisation of monotone ill-posed problems
Markus Grasmair, Fredrik Hildrum
We introduce subgradient-based Lavrentiev regularisation of the form \begin{equation*} \mathcal{A}(u) + α\partial \mathcal{R}(u) \ni f^δ\end{equation*} for linear and nonlinear ill…
Source Conditions for non-quadratic Tikhonov Regularisation
Markus Grasmair
In this paper we consider convex Tikhonov regularisation for the solution of linear operator equations on Hilbert spaces. We show that standard fractional source conditions can be…
Variational Inequalities and Improved Convergence Rates for Tikhonov Regularisation on Banach Spaces
Markus Grasmair
In this paper we derive higher order convergence rates in terms of the Bregman distance for Tikhonov like convex regularisation for linear operator equations on Banach spaces. The…
An Approach to the Minimization of the Mumford-Shah Functional using Γ-convergence and Topological Asymptotic Expansion
Markus Grasmair, Monika Muszkieta, Otmar Scherzer
In this paper, we present a method for the numerical minimization of the Mumford-Shah functional that is based on the idea of topological asymptotic expansions. The basic idea is t…
The Residual Method for Regularizing Ill-Posed Problems
Markus Grasmair, Markus Haltmeier, Otmar Scherzer
Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply con…