3 citations · 5 across the 5 of their papers we have counts for
6 papers
Asymptotic Expansions for Higher Order Elliptic Equations with an Application to Quantitative Photoacoustic Tomography
Andrea Aspri, Elena Beretta, Otmar Scherzer +1
In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological…
A duality based approach to the minimizing total variation flow in the space
Yoshikazu Giga, Monika Muszkieta, Piotr Rybka
We consider a gradient flow of the total variation in a negative Sobolev space under the periodic boundary condition. If , the flow is nothing but…
A variational method for quantitative photoacoustic tomography with piecewise constant coefficients
Elena Beretta, Monika Muszkieta, Wolf Naetar +1
In this article, we consider the inverse problem of determining spatially heterogeneous absorption and diffusion coefficients from a single measurement of the absorbed energy (in t…
A variational algorithm for the detection of line segments
E. Beretta, M. Grasmair, M. Muszkieta +1
In this paper we propose an algorithm for the detection of edges in images that is based on topological asymptotic analysis. Motivated from the Mumford--Shah functional, we conside…
Two cases of squares evolving by anisotropic diffusion
Piotr B. Mucha, Monika Muszkieta, Piotr Rybka
We are interested in an anisotropic singular diffusion equation in the plane and in its regularization. We establish existence, uniqueness and basic regularity of solutions to both…
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…