Optimal control techniques for thermo-acoustic tomography

Thermo-acoustic and photo-acoustic tomography are imaging techniques that combine high electromagnetic absorption contrast between two media with ultrasound high resolution. Both techniques lead to an ill-posed inverse problem of the same form which entails inversion (in the wide sense) of the spherical Radon transform. One currently has a choice between three main types of reconstruction procedures namely the filtered backprojection formulae, eigenfunction expansion methods and time reversal method. In this paper we propose to investigate this inverse problem with an alternative control formulation : in our model the function to be recovered is the control function while the (acoustic) pressure is the state function which satisfies a wave equation. We stress that our objective is to give modelling hints, and not to provide new results. Otherwise expressed, the originality of this paper lies essentially in the way the problem is stated