Abstract:

Optical tomography is a useful medical imaging modality because of the high contrast between healthy and non-healthy tissues. However, it suffers from poor resolution. Ultrasound tomography enjoys very high resolution capabilities but suffers from low contrast. Photo-acoustic tomography (PAT) is a novel imaging technique that aims to combine the best of both modalities. Propagating radiation heats up the underlying medium, which emits acoustic waves by mechanical expansion. The absorption map is reconstructed from the high resolution acoustic waves. The high optical contrast is then reconstructed from the absorption map.

PAT is an example of a hybrid imaging modality. Other such modalities include thermo-acoustic tomography (TAT) and acousto-optics tomography (AOT). Mathematically, these modalities require that one solve inverse problems for partial differential equations (PDE) from availability of internal functionals of the the PDE solutions. This talk will present recent uniqueness and stability results in the context of elliptic and transport equations as they arise, e.g., in PAT, TAT, and AOT. We present theoretical and numerical evidence that, ideally, these hybrid modalities offer superior reconstructions to the "single" modalities taken separately.