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 …

The purpose of this chapter is to provide a survey of our book by placing what we have to
say in a historical context. We obviously cannot give a complete account of inverse …

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 introduce a method to recover a continuous domain representation of a piecewise
constant two-dimensional image from few low-pass Fourier samples. Assuming the edge set …

This book is the first to comprehensively explore elasticity imaging and examines recent,
important developments in asymptotic imaging, modeling, and analysis of deterministic and …

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 …

The level set approach has proven widely successful in the study of inverse problems for
interfaces, since its systematic development in the 1990s. Recently it has been employed in …