  We present a comprehensive study on how well gravitational-wave signals of
binary black holes with nonzero eccentricities can be recovered with state of
the art model-independent waveform reconstruction and parameter estimation
techniques. For this we use BayesWave, a Bayesian algorithm used by the
LIGO-Virgo Collaboration for unmodeled reconstructions of signal waveforms and
parameters. We used two different waveform models to produce simulated signals
of binary black holes with eccentric orbits and embed them in samples of
simulated noise of design-sensitivity Advanced LIGO detectors. We studied the
network overlaps and point estimates of central moments of signal waveforms
recovered by BayesWave as a function of $e$, the eccentricity of the binary at
8 Hz orbital frequency. BayesWave recovers signals of near-circular
($e\lesssim0.2$) and highly eccentric ($e\gtrsim0.7$) binaries with network
overlaps similar to that of circular ($e=0$) ones, however it produces lower
network overlaps for binaries with $e\in[0.2,0.7]$. Estimation errors on
central frequencies and bandwidths (measured relative to bandwidths) are nearly
independent from $e$, while estimation errors on central times and durations
(measured relative to durations) increase and decrease with $e$ above
$e\gtrsim0.5$, respectively. We also tested how BayesWave performs when
reconstructions are carried out using generalized wavelets with linear
frequency evolution (chirplets) instead of sine-Gaussian wavelets. We have
found that network overlaps improve by $\sim 10-20$ percent when chirplets are
used, and the improvement is the highest at low ($e<0.5$) eccentricities. There
is however no significant change in the estimation errors of central moments
when the chirplet base is used.
