Thermoacoustic Tomography in Elastic Media

Justin Tittelfitz
University of Washington

Room: REC103

Jan 23, 2013 3:30 PM EST

In this talk, we will discuss an emerging method of medical imaging known as thermoacoustic tomography. Mathematically, the problem is that of recovering the initial displacement f for a solution u of a wave equation in [0,T] × \mathbb{R}sup>3, given measurements of u on [0,T] × ∂Ω, where Ω⊂ \mathbb{R}3$ is some bounded domain containing the support off. This problem is relatively well-understood in acoustic media (i.e. for a scalar wave equation), but less is known about the problem in elastic media. In this talk, I will discuss this case; specifically, we assume u = (u1<\sub>,u2,u3) solves the isotropic elastic wave equation ∂t2 u = ∇ ⋅ (μ(x) ((∇ u) + (∇ u)T)) + ∇ (λ(x) ∇ ⋅u), and discuss sufficient conditions on the Lamè parameters μ and λ to ensure recovery of f is possible. If time permits, I will also discuss some of the related numerical work, showing the results of performing the reconstruction process with simulated data.