This review is devoted to some inverse problems arising in the context of linear elasticity,
namely the identification of distributions of elastic moduli, model parameters or buried …

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 main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

The topological derivative is defined as the first term (correction) of the asymptotic expansion
of a given shape functional with respect to a small parameter that measures the size of …

Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems is the first
book in which two new concepts of numerical solutions of multidimensional Coefficient …

The factorization method is a relatively new method for solving certain types of inverse
scattering problems and problems in tomography. Aimed at students and researchers in …

The level-set method has been recently introduced in the field of shape optimization,
enabling a smooth representation of the boundaries on a fixed mesh and therefore leading …

This book has grown out of lecture notes for a course on mathematical methods in
biomedical imaging at Ecole Polytechnique. Biomedical imaging is a fascinating research …

In multistatic imaging one uses waves to probe for information about an unknown medium.
These waves can be acoustic, elastic, or electromagnetic. They can be at zero-frequency …

Since the early part of the twentieth century, the use of integral equations has developed into
a range of tools for the study of partial differential equations. This includes the use of single …