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Improved Binary Black Hole Search Discriminator from the Singular Value Decomposition of Non-Gaussian Noise Transients

Tathagata Ghosh, Sukanta Bose, Sanjeev Dhurandhar, Sunil Choudhary

Abstract

The sensitivity of current gravitational wave (GW) detectors to transient GW signals is severely affected by a variety of non-Gaussian and non-stationary noise transients, such as the blip, tomte, koi fish, and low-frequency blip 'glitches'. These glitches share some time-frequency resemblance with GW signals from binary black holes. In earlier works [Joshi et al., Phys. Rev. D 103, 044035 (2021); Choudhary et al., Phys. Rev. D 110, 044051 (2024)], the authors presented a method for constructing a $χ^2$-distributed optimized statistic, based on the unified formalism of $χ^2$ discriminators [Dhurandhar et al., Phys. Rev. D 96, 103018 (2017)], to distinguish the blip glitches from the compact binary coalescence (CBC) signals. Unlike past works, the new $χ^2$ discriminator is constructed from the most significant singular vectors obtained from the singular value decomposition of different classes of glitches in real detector data. We find that the chi-square developed in this work performs as efficiently as in Choudhary et al. [Phys. Rev. D 110, 044051 (2024)], which used sine-Gaussian basis vectors. This result supports past empirical findings that these glitches are reasonably well-modeled by sine-Gaussians. It also introduces a method for constructing signal- and glitch-based $χ^2$ discriminators by directly using real data containing the glitches and, thus, holds promise for extensions to glitches that are captured less well by sine-Gaussians or other analytical functions.

Improved Binary Black Hole Search Discriminator from the Singular Value Decomposition of Non-Gaussian Noise Transients

Abstract

The sensitivity of current gravitational wave (GW) detectors to transient GW signals is severely affected by a variety of non-Gaussian and non-stationary noise transients, such as the blip, tomte, koi fish, and low-frequency blip 'glitches'. These glitches share some time-frequency resemblance with GW signals from binary black holes. In earlier works [Joshi et al., Phys. Rev. D 103, 044035 (2021); Choudhary et al., Phys. Rev. D 110, 044051 (2024)], the authors presented a method for constructing a -distributed optimized statistic, based on the unified formalism of discriminators [Dhurandhar et al., Phys. Rev. D 96, 103018 (2017)], to distinguish the blip glitches from the compact binary coalescence (CBC) signals. Unlike past works, the new discriminator is constructed from the most significant singular vectors obtained from the singular value decomposition of different classes of glitches in real detector data. We find that the chi-square developed in this work performs as efficiently as in Choudhary et al. [Phys. Rev. D 110, 044051 (2024)], which used sine-Gaussian basis vectors. This result supports past empirical findings that these glitches are reasonably well-modeled by sine-Gaussians. It also introduces a method for constructing signal- and glitch-based discriminators by directly using real data containing the glitches and, thus, holds promise for extensions to glitches that are captured less well by sine-Gaussians or other analytical functions.

Paper Structure

This paper contains 8 sections, 10 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Matched filtering
  3. The unified $\chi^{2}$ formalism
  4. Singular value decomposition (SVD)
  5. Constructing SVD-based $\chi^{2}$ discriminators
  6. Preparation for $\chi^{2}$ calculation
  7. Results
  8. Conclusion

Figures (8)

  • Figure 1: The first four rows show the first three singular vectors obtained from $100$ glitches of each class---blip, tomte, koi fish, and low-frequency blip, respectively. The bottom row shows the first three singular vectors obtained by performing an SVD on the $12$ singular vectors displayed in the panels above.
  • Figure 2: A simulated CBC signal added to real detector strain data. Top-right panel: The SNR time series obtained by matched filtering real GW data with a simulated CBC signal added to it. The template used for producing it was the loudest one, in this time-stretch, from the aligned-spin template bank with component mass between $30~M_{\odot}$ and $40~M_{\odot}$. Here, the peak matched-filter SNR is $14.7$. Bottom-right panel: SV-SNR (discussed in section \ref{['sec:chisq_prepare']} time series for the same simulated CBC signal, with the peak SNR of $8.2$. Note that the time of the peak SNR is different in the two right plots (see Bose:2016jeo for an explanation). Left panel: The time-frequency plot of a CBC signal is shown to illustrate the lag between the time the CBC template is triggered (indicated by the vertical dot-dashed magenta line, at a later time) and the blip singular vectors are triggered (shown by the vertical dashed orange line, at an earlier time).
  • Figure 3: A blip glitch in real GW strain data. Left panel: Time-frequency plot of the blip glitch.Top-right panel: The SNR time series plot of the blip glitch obtained by matched-filtering with the loudest CBC template that was triggered by this time-stretch. The CBC template bank employed here was identical to the one used in figure \ref{['fig:cbc_trigger_time']}. The peak value of the matched-filter SNR is $13.1$. Bottom-right panel: SV-SNR time series for the same blip glitch, with the peak SNR of $23$.
  • Figure 4: ROC curves showing the performance of various $\chi^{2}$ statistics for different glitch classes---blip, tomte, koi fish, and low-frequency blip (left to right columns)---evaluated using CBC signals in different mass ranges, as indicated on the right of the respective panels.
  • Figure 5: Volume–time sensitivity (VT) as a function of inverse false-alarm rate (iFAR) for different $\chi^{2}$ statistics, shown for two mass bins: $m_{1,2} \in [20,30]~M_{\odot}$ and $m_{1,2} \in [50,60]~M_{\odot}$.
  • ...and 3 more figures