Reconstruction and stability in acousto-optic imaging for absorption maps with bounded variation

Habib Ammari , Loc Hoang Nguyen , L. Seppecher (1, 2, 3, 4)

1 UCBL - Université Claude Bernard Lyon 1
2 ECL - École Centrale de Lyon
3 MMCS - Modélisation mathématique, calcul scientifique
4 ICJ - Institut Camille Jordan

The aim of this paper is to propose for the first time a reconstruction scheme and a stability result for recovering from acoustic-optic data absorption distributions with bounded variation. The paper extends earlier results in [3] and [5] on smooth absorption distributions. It opens a door for a mathematical and numerical framework for imaging, from internal data, parameter distributions with high contrast in biological tissues.

Mots clés: acousto-optic tomography; parameter with bounded variation; reconstruction; stability; imaging biological tissues

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Analyse numérique [math.NA]; Imagerie

Habib Ammari, Loc Hoang Nguyen, L. Seppecher. Reconstruction and stability in acousto-optic imaging for absorption maps with bounded variation. Journal of Functional Analysis, 2014, ⟨10.1016/j.jfa.2014.09.029⟩. ⟨hal-03628613⟩