  A vitally important requirement for detecting gravitational wave (GW) signals
from compact coalescing binaries (CBC) with high significance is the reduction
of the false-alarm rate of the matched-filter statistic. The data from GW
detectors contain transient noise artifacts, or glitches, which adversely
affect the performance of search algorithms by producing false alarms. Glitches
with large amplitudes can produce triggers in the SNR time-series in spite of
their small overlap with the templates. This contributes to false alarms.
Historically, the traditional $\chi^2$ test has proved quite useful in
distinguishing triggers arising from CBC signals and those caused by glitches.
In a recent paper, a large class of unified $\chi^2$ discriminators was
formulated, along with a procedure to construct an optimal $\chi^2$
discriminator, especially, when the glitches can be modeled. A large variety of
glitches that often occur in GW detector data can be modeled as sine-Gaussians,
with quality factor and central frequency, ($Q,f_0$), as parameters. We use
Singular Value Decomposition to identify the most significant degrees of
freedom in order to reduce the computational cost of our $\chi^2$. Finally, we
construct a $\chi^2$ statistic that optimally discriminates between
sine-Gaussian glitches and CBC signals. We also use
Receiver-Operating-Characteristics to quantify the improvement in search
sensitivity when it employs the optimal $\chi^2$ compared to the traditional
$\chi^2$. The improvement in detection probability is by a few to several
percentage points, near a false-alarm probability of a few times $10^{-3}$, and
holds for binary black holes (BBHs) with component masses from several to a
hundred solar masses. Moreover, the glitches that are best discriminated
against are those that are like sine-Gaussians with $Q\in [25,50]$ and $f_0\in
[40,80]$Hz.
