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We give an overview of recent techniques which use a level set representation of shapes for
solving inverse scattering problems. The main focus is on electromagnetic scattering using …

Interface problems arise in many applications. For example, when there are two different
materials, such as water and oil, or the same material but at different states, such as water …

The aim of this paper is to investigate the use of topological derivatives in combination with
the level set method for shape reconstruction and optimization problems. We propose a new …

The aim of this paper is to provide a survey on the recent development in level set methods
in inverse problems and optimal design. We give introductions on the general features of …

The aim of this paper is to develop a functional-analytic framework for the construction of
level set methods, when applied to shape optimization and shape reconstruction problems …

In this paper, we propose a numerical scheme for the identification of piecewise constant
conductivity coefficient for a problem arising from electrical impedance tomography. The key …

We propose a level set approach for elliptic inverse problems with piecewise constant
coefficients. The geometry of the discontinuity of the coefficient is represented implicitly by …

This paper is devoted to the solution of shape reconstruction problems by a level set
method. The basic motivation for the setup of this level set algorithm is the well-studied …

In this paper, a parametric level set method for reconstruction of obstacles in general inverse
problems is considered. General evolution equations for the reconstruction of unknown …