Application of dictionary learning to denoise LIGO's blip noise transients

Abstract: Data streams of gravitational-wave detectors are polluted by transient noise features, or "glitches", of instrumental and environmental origin. In this work, we investigate the use of total-variation methods and learned dictionaries to mitigate the effect of those transients in the data. We focus on a specific type of transient, "blip" glitches, as this is the most common type of glitch present in the LIGO detectors and their waveforms are easy to identify. We randomly select 80 blip glitches scattered in the data from advanced LIGO's O1 run, as provided by the citizen-science project Gravity Spy. Our results show that dictionary-learning methods are a valid approach to model and subtract most of the glitch contribution in all cases analyzed, particularly at frequencies below $\sim 1$ kHz. The high-frequency component of the glitch is best removed when a combination of dictionaries with different atom length is employed. As a further example, we apply our approach to the glitch visible in the LIGO-Livingston data around the time of merger of binary neutron star signal GW170817, finding satisfactory results. This paper is the first step in our ongoing program to automatically classify and subtract all families of gravitational-wave glitches employing variational methods.

• The paper demonstrates that dictionary learning combined with total variation methods effectively reduces LIGO's blip noise transients.
• It employs sparse reconstruction using ADMM and optimized dictionary training on 100 blip glitches to enhance signal fidelity.
• The approach notably improved noise mitigation across different frequency ranges, as evidenced by successful application to the GW170817 event.

Application of Dictionary Learning to Denoise LIGO's Blip Noise Transients

Introduction

Data from gravitational-wave (GW) detectors like LIGO are often contaminated by non-astrophysical noise transients known as "glitches." This study investigates the efficacy of dictionary learning techniques in mitigating these glitches, focusing on "blip" glitches, which are prevalent in LIGO data. The researchers apply total variation methods and learned dictionaries to model and subtract the glitch contribution in the GW signal, attempting to enhance the significance of astrophysical triggers.

Variational Methodologies

Total Variation Methods

The paper employs two variational techniques based on the $\text{L}_1$ norm: the Rudin-Osher-Fatemi (ROF) method and a Dictionary Learning method. The denoising problem is formulated as a variational problem $y=u+n$, where $u$ represents the true signal and $n$ the noise. The ROF method uses a total variation-based regularization to remove noise while preserving significant signal gradients:

$$u_{\lambda} = \underset{u}{\text{argmin}} \left\{ \int_\Omega |\nabla u|+\frac{\lambda}{2} ||y-u||^2 \right\}$$

where $\lambda$ is a regularization parameter controlling the trade-off between preserving data fidelity and regularization.

Sparse Reconstruction Using Fixed Dictionaries

In dictionary-based denoising, the signal $u$ is assumed to be a sparse combination of dictionary atoms $\bm{D}$, optimized via:

$$\alpha_{\lambda} = \underset{\alpha}{\rm{argmin}} \left\{ |\alpha|+\frac{\lambda}{2}||\bm{D}\alpha- y||^2\right\}$$

This study leverages the Alternating Direction Method of Multipliers (ADMM) for sparse coding, ensuring convexity through the $\text{L}_1$ regularization.

Dictionary Learning

The approach not only uses predefined dictionaries but also learns dictionaries from data. This enhances signal representation quality by adapting to signal characteristics:

$$\alpha_{\lambda}, \bm{D}_{\lambda} = \underset{\alpha, \bm{D}}{\rm{argmin}} \left\{\frac{1}{n}\sum_{i=1}^{m}||\bm{D}\alpha_i- {x}_i||^2_2+\lambda|\alpha_i|\right\}$$

The optimized approach uses stochastic approximations to efficiently update dictionaries during training.

Data Selection and Training

Random samples of 100 blip glitches were selected for training and testing from LIGO's first observing run. Utilizing whitening procedures and a rigorously structured training approach, dictionaries were formulated to optimally represent the blip glitches in real detector noise.

Figure 1: Example of a dictionary composed by a total of 192 atoms with 128 samples each. Only 16 atoms randomly selected are shown.

Results

Blip Glitch Mitigation

The methodologies tested various dictionary lengths ($2^3$ to $2^9$ samples per atom) and found that combining dictionaries with different atom lengths optimized high-frequency noise removal.

Figure 2: Time-series plots of three illustrative examples of blip glitches, corresponding to numbers 7, 9, and 15 from the test set.

Using a single dictionary effectively mitigated low-frequency glitches, while combining dictionaries improved high-frequency noise subtraction, as highlighted by SNR improvements.

Application to GW170817

Applying the learned dictionary approach to the GW170817 merger event resulted in successful removal of instrumental noise without affecting the GW signal itself. Despite differing glitch characteristics, this demonstrated the approach's robustness.

Figure 3: Time-frequency diagram of 8 seconds of data corresponding to the GW170817 signal.

Conclusion

The application of dictionary learning to transient noise reduction showcases potential for improving GW data analysis integrity. The combination of multiple dictionaries proved advantageous, particularly at high frequencies, signifying broad applicability to diverse noise families. Advancements in computational efficiency and dictionary customization might further enhance real-time GW detection capabilities. The research suggests possibilities for dictionary-trained models to aid low-latency pipelines in future GW observatories.