Mathematics and its Applications Seminar
Alison Malcolm
Massachusetts Institute of Technology
Simulating nonlinear imaging
Abstract: The majority of imaging technologies are sensitive to the linear
properties of the imaged medium, for example Computed Tomography is
sensitive to X-ray absorption and seismic imaging is sensitive to
changes in wave velocity. When differentiating between healthy and
cancerous tissue in medical imaging or oil and water in Earth
imaging, there is growing evidence that contrasts in nonlinear
material properties can also provide important information. A
particular example is Ultrasound Vibro-Acoustography, in which the
nonlinear interaction of ultrasound waves at multiple frequencies is
used to generate images sensitive to both linear and nonlinear
material parameters. Creating and testing a mathematical model of
this experiment presents many computational challenges, arising from
the range of scales and the intrinsic nonlinearity of the problem.
To address these challenges, we have developed a set of integral
equation methods specifically tailored to this problem, allowing the
rapid, accurate, simulation of the experiment.
Wednesday November 18, 2009 at 4:00 PM in SEO 636