Nonlinear Independent Component Analysis Scheme and its application to gravitational wave data analysis

Abstract

Noise subtraction is a crucial process in gravitational wave (GW) data analysis to improve the sensitivity of interferometric detectors. While linear noise coupling has been extensively studied and successfully mitigated using methods such as Wiener filtering, subtraction of non-linearly coupled and non-stationary noise remains a significant challenge. In this work, we propose a novel independent component analysis (ICA)-based framework designed to address non-linear coupling in noise subtraction. Building upon previous developments, we derive a method to estimate general quadratic noise coupling while maintaining computational transparency compared to machine learning approaches. The proposed method is tested with simulated data and real GW strain data from KAGRA. Our results demonstrate the potential of this framework to effectively mitigate complex noise structures, providing a promising avenue for improving the sensitivity of GW detectors.

Figures (6)

• Figure 1: ASD of the data which only includes the noise components. The three curves correspond to: raw data (blue), the result after applying the slow approximation method (green), and the result after applying the non-linear ICA (orange).
• Figure 2: Left panel: Absolute value of the estimated kernel, $|K_{12}|$, which quantifies the coupling between two channels in the frequency domain. Right panel: Bi-coherence $r_{012}$, which measures the statistical significance of the observed non-linear coupling.
• Figure 3: (Left panel) Normalized Fourier amplitude $\propto |\tilde{d}(f)|$ (solid curves) and the estimated noise ASD (dashed lines) around the injected signal frequency $f_s$, for both the raw data (blue) and the cleaned data (orange). The injected signal appears as a prominent peak in the raw data, which is increased after cleaning. (Right panel) Matched-filter SNR for the injected signal, plotted for the raw data (dashed blue) and the cleaned data (solid orange).
• Figure 4: (Left panel) Change in SNR before (horizontal axis) and after (vertical axis) ICA, for 100 realizations of the injected signal with randomly chosen phase $\phi \in [0,2\pi]$. Each point is color-coded by the corresponding signal phase. (Right panel) Histogram of the fractional change in SNR across all realizations. The vertical dashed lines mark the mean, mean $\pm$ standard deviation, with the mean value showing a 13% improvement and the worst-case degradation being only about 3.4%.
• Figure 5: ASDs of witness sensors in the arbitrary unit. The left panel shows the fast component around the injected frequency $f = 590.1$Hz while the right panel presents the slow modes, which generate sidebands in the main channel through the bi-linear coupling.