They constitute a class of inverse problems where several physical
modalities are cleverly combined to transform an ill-posed problem into a stable one. Typically,
the medium is probed with a type of waves which is highly sensitive to the contrast in its material
coefficients, albeit being too diffusive to allow reconstruction, while another type of waves is used
to convey the response to the probe to where it can be measured. This is the case of photo-
acoustic imaging for instance, where pressure waves are monitored, that result from the dilation
of absorbing tissues by a laser excitation. Understanding what makes these techniques stable and
what determines their resolution is a challenge we would like to tackle.
