A MUSIC-type Algorithm for Detecting Internal Corrosion from Electrostatic Boundary Measurements

Habib Ammari (1) , Hyeonbae Kang (2) , Eunjoo Kim (2) , Kaouthar Louati (3, 4) , Michael S. Vogelius (5)

1 LOA - Laboratoire Ondes et Acoustique (UMR 7587)
2 Department of Mathematical Sciences
3 CMAP - Centre de Mathématiques Appliquées
4 MODAL'X - Modélisation aléatoire de Paris X
5 Department of Mathematics - Rutgers School of Arts and Sciences

We establish an asymptotic representation formula for the steady state currents caused by internal corrosive parts of small Hausdorff measures. Based on this formula, we design a non-iterative method of MUSIC (multiple signal classification) type for localizing the corrosive parts from voltage-to-current observations.

Mots clés: corrosion; asymptotic representation formula; reconstruction; layer potentials

Domaines: Analyse classique [math.CA]; Mathématiques générales [math.GM]

Habib Ammari, Hyeonbae Kang, Eunjoo Kim, Kaouthar Louati, Michael S. Vogelius. A MUSIC-type Algorithm for Detecting Internal Corrosion from Electrostatic Boundary Measurements. 2007. ⟨hal-00125787v1⟩