|Location:||MSRI: Simons Auditorium|
Consider the problem of imaging a reflector (target) from
recordings of the echoes resulting from probing the medium with waves
emanating from an array of transducers (the array response matrix).
We present an algorithm that selectively illuminates the edges or the
interior of an extended target by choosing particular subspaces of
the array response matrix. For a homogeneous background medium, we
characterize these subspaces in terms of the singular functions of a
space and wave number restricting operator, which are also called
generalized prolate spheroidal wave functions. We discuss results
indicating what can be expected from using this algorithm when the
medium fluctuates around a constant background medium and the
fluctuations can be modeled as a random field.