  A world-wide array of highly sensitive interferometers stands poised to usher
in a new era in astronomy with the first direct detection of gravitational
waves. The data from these instruments will provide a unique perspective on
extreme astrophysical phenomena such as neutron stars and black holes, and will
allow us to test Einstein's theory of gravity in the strong field, dynamical
regime. To fully realize these goals we need to solve some challenging problems
in signal processing and inference, such as finding rare and weak signals that
are buried in non-stationary and non-Gaussian instrument noise, dealing with
high-dimensional model spaces, and locating what are often extremely tight
concentrations of posterior mass within the prior volume. Gravitational wave
detection using space based detectors and Pulsar Timing Arrays bring with them
the additional challenge of having to isolate individual signals that overlap
one another in both time and frequency. Promising solutions to these problems
will be discussed, along with some of the challenges that remain.
