Denoising gravitational wave with deep learning in the time-frequency domain

TL;DR

The paper addresses denoising gravitational-wave signals in the time-frequency domain to extract BBH merger events from noisy LIGO data. It proposes a two-stage model combining an amplitude denoising autoencoder with a Griffin-Lim–inspired phase reconstruction network, using an amplitude mask to steer phase recovery. The authors generate a training dataset by injecting SEOBNRv4 waveforms into Hanford noise, applies STFT to a $32\times 64$ representation, and train with transfer and curriculum learning, reporting about 74% of 14,399 mock injections achieving an overlap above 0.8 and good merger-stage alignment for real O3a events. The results suggest a promising direction for gravitational-wave data analysis and point to avenues for future work, including incorporating spins and alternative waveform families, exploring wavelet transforms, and integrating attention-like mechanisms.

Abstract

Gravitational wave denoising is an ongoing task for revealing the events of compact binary objects in the universe. Recently, with the aid of deep learning, gravitational waves have been efficiently and delicately extracted from the noisy data compared with the traditional match-filtering. While most of the relevant studies adopt the data in the time series only, the time-frequency data processing is also in progress due to its several advantages for the waveform denoising. Here, we target the gravitational waves events emitted by binary black hole (BBH) mergers, with their total mass larger than 30 solar masses. For denoising, we propose a deep learning model utilizing the Griffin-Lim algorithm, an existing numerical approach to restore the phase information from the related amplitude spectrogram. This design allows extra attention on the phase recovery by using a priorly denoised amplitude spectrogram. The denoising results fit well in both the amplitude and the phase alignments of the mock injected waveforms. We also apply our model to the real detected events and discover a nice consistency with the simulated template waveforms, especially the high accuracy around the merger stage. Our work suggests the possibility of a better methodological design for gravitational wave data analysis.

Figures (10)

• Figure 1: Visualizing the Griffin-Lim algorithm. The function of each block is described in the context. We note that Eq. (\ref{['glmask']}) in this paper is the same as in the second block of the iteration.
• Figure 2: Data preprocessing for the time-frequency denoising. The procedure demonstrates how the noise and the waveform are combined into the training data and the target of the deep learning model. The time-frequency panels consist of the real and the imaginary parts, which are plotted in the upper-left and lower-right, respectively.
• Figure 3: The denoising deep learning model architecture, which can be divided into (a) the amplitude autoencoder and (b) the Griffin-Lim network. The dashed and solid lines with arrows represent the amplitude and the real-imaginary data flow, respectively. Note that there are two inputs for the GL mask, one is the amplitude and the other is the real-imaginary data, as suggested in Eq. (\ref{['glmask']}).
• Figure 4: The workflow of denoising an injected gravitational wave event. We specify the important stages, (a) raw detector data segment with a gravitational wave signal, (b) preprocessed data, (c) the denoised amplitude spectrogram, (d) the binary amplitude mask calculated from (c), (e) the model input after begin masked by (e), (f) the denoised waveform, and (g) the target waveform. The frames of the panels indicate the current processing representation. The arrows between the panels point out the direction of the data flow. The real and the imaginary parts are respectively placed on the upper-left and the lower-right in the second column. There are no time series or real-imaginary spectrograms of stage (c) and (d). Only the frequency axes of the time-frequency spectrograms of (a) are plotted in the logarithm scale for a better visualization.
• Figure 5: Statistics of the 14,399 denoised injected mock events. (a) Distribution of the mass parameters of the mock test set. The masses are in the unit of solar mass. The missing population in the lower-left corner is due to the exclusion of the events with small total masses. (b) Relation between the SNR and the overlap. It can be observed that large SNR is more likely to result in large overlap.