Ting Zhou
SPECIAL MATHEMATICS COLLOQUIUM
Speaker: Ting Zhou Abstract. TAT is an example of a coupled-physics modality, which combines the high contrast of a physical phenomenon (here the electrical properties of tissues) with the high resolution of another phenomenon (here ultrasound). Thermo-acoustic imaging may be decomposed into two steps. The first step aims at reconstructing an amount of electromagnetic radiation absorbed by tissues from boundary measurements of ultrasound signals generated by these radiations. We assume this first step done. Quantitative thermo-acoustics then consists of reconstructing the conductivity coefficient in the equation from the now known absorbed radiation. This second step is the problem of interest in this work. Mathematically, quantitative thermo-acoustics consists of reconstructing the conductivity in time-harmonic Maxwell's equations from available internal data that are linear in the conductivity and quadratic in the electric field. We consider inverse problems of this type with applications in thermo-acoustics. In this framework, we obtain uniqueness and stability of the reconstruction for a scalar model of time-harmonic wave propagation, by choosing appropriate illuminations known as complex geometric optics (CGO) solutions for the equation. At last but not least, we consider the full system models of Maxwell's equations and see a different flavor of analysis of uniqueness and stability using CGO solutions. These are joint works with Guillaume Bal, Kui Ren and Gunther Uhlmann. |