  In dense stellar regions, highly eccentric binaries of black holes and
neutron stars can form through various n-body interactions. Such a binary could
emit a significant fraction of its binding energy in a sequence of largely
isolated gravitational wave bursts prior to merger. Given expected black hole
and neutron star masses, many such systems will emit these repeated bursts at
frequencies within the sensitive band of contemporary ground-based
gravitational wave detectors. Unfortunately, existing gravitational wave
searches are ill-suited to detect these signals. In this work, we adapt a
"power stacking" method to the detection of gravitational wave signals from
highly eccentric binaries. We implement this method as an extension of the
Q-transform, a projection onto a multiresolution basis of windowed complex
exponentials that has previously been used to analyze data from the network of
LIGO/Virgo detectors. Our method searches for excess power over an ensemble of
time-frequency tiles. We characterize the performance of our method using Monte
Carlo experiments with signals injected in simulated detector noise. Our
results indicate that the power stacking method achieves substantially better
sensitivity to eccentric binary signals than existing localized burst searches.
