Inverse Transport Problems and Photoacoustics

Inverse transport consists of reconstructing the optical parameters in a transportequation from knowledge of a measurement operator. We review several uniqueness andstability results obtained in the context of various boundary measurements as they arisee.g. in optical tomography, a medical imaging modality. Accurate numerical reconstructionsobtained by carefully capturing the singularities of the measurement operator are also brieflypresented.In many practical settings, the typical boundary measurements available in inversetransport do not allow us to reconstruct the optical parameters with sufficient resolution.In the second part of the talk, I present recent results obtained for the inverse trans-port problem with internal controls as they arise in the application of photoacoustic to-mography, a recent hybrid medical imaging modality that combines the large contrastobserved in optical parameters with the high resolution of ultrasounds.