In time-reversal acoustics a signal is recorded by an array of
transducers, time-reversed and then re-transmitted into the medium. The
re-transmitted signal propagates back through the same medium and
refocuses approximately on the source. The possibility of refocusing by
time-reversal has many important applications in medicine, geophysics,
non-destructive testing, underwater acoustics, wireless communications,
etc. In a homogeneous medium, the refocusing resolution of the
time-reversed signal is determined by the diffraction limit. When the
medium has random inhomogeneities the resolution of the refocused signal
can in some circumstances beat the diffraction limit, called
super-resolution. I will talk about some theoretical analysis of this
phenomena as well as numerical challenges in the simulation. Applications
to imaging will be discussed if time permits.
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