Radar and sonar, satellite observations
CAT scans, indeed most of medical imaging,
are ubiquitous examples of the recovery of a hidden
or remote object by making measurements from a distance.
They are wonderful case studies of the application of mathematics.
In all such problems there is a partial differential equation
lurking behind the scenes. If we knew the shape, location
and material properties of the object then mathematics developed
in the latter half of the nineteen century and first half of the
twentieth would let us predict, in theory, exactly the kind
of measurements we would obtain.
The much harder, but interesting part, is the converse; given the measurements, where, and what, is the object? This talk will explore this inverse problem, specifically the issues of uniqueness and determination. What is the least amount of measurements one can make in order to obtain a unique recovery? Are there algorithms that would let us reconstruct the object and what are their limitations? And, of course, what are the pdes and what makes these problems so challenging from an analysis viewpoint?
Back to colloquium page