An optimal control approach to photoacoustic tomography

Maîtine Bergounioux (1) , Thomas Haberkorn (1) , Yannick Privat (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 LJLL - Laboratoire Jacques-Louis Lions

Quantitative photoacoustic tomography is a hybrid imaging technique for soft tissues. It consists in exciting the body to reconstruct with a laser pulse and measuring the induced acoustic waves due to the inhomogenous heating and then expansion of the tissues. We present a simplified mathematical model of this phenomenon, which writes as a system of two coupled equations, namely a wave equation and a diffusion approximation of a radiative transfer equation. Following [5], the inverse problem of reconstructing the optical absorption coefficient is written as an optimal control problem where the control is the parameter we seek to reconstruct. Necessary conditions for optimality of a control and numerical results for this approach are given in the case of a small number of sensors.

Domaines: Equations aux dérivées partielles [math.AP]

Maîtine Bergounioux, Thomas Haberkorn, Yannick Privat. An optimal control approach to photoacoustic tomography. 55th IEEE Conference on Decision and Control, Dec 2016, Las Vegas, France. pp.1620 - 1624, ⟨10.1109/CDC.2016.7798497⟩. ⟨hal-01582986⟩