  Stellar-mass black hole binaries (BHBs) in galactic nuclei are
gravitationally perturbed by the central supermassive black hole (SMBH) of the
host galaxy, potentially inducing strong eccentricity oscillations through the
eccentric Kozai-Lidov (EKL) mechanism. These highly eccentric binaries emit a
train of gravitational-wave (GW) bursts detectable by the Laser Interferometer
Space Antenna (LISA) -- a planned space-based GW detector -- with
signal-to-noise ratios (SNRs) up to ${\sim}100$ per burst. In this work, we
study the GW signature of BHBs orbiting our galaxy's SMBH, Sgr A$^*$, which are
consequently driven to very high eccentricities. We demonstrate that an
unmodeled approach using a wavelet decomposition of the data effectively yields
the time-frequency properties of each burst, provided that the GW frequency
peaks between $10^{-3}\,\,\mathrm{Hz}$--$10^{-1}\,\,\mathrm{Hz}$. The wavelet
parameters may be used to infer the eccentricity of the binary, measuring
$\log_{10}(1-e)$ within an error of $20\%$. Our proposed search method can thus
constrain the parameter space to be sampled by complementary Bayesian inference
methods, which use waveform templates or orthogonal wavelets to reconstruct and
subtract the signal from LISA data.
