Reconstruction of Black Hole Ringdown Signals with Data Gaps using a Deep-Learning Framework

TL;DR

Reconstruction of Black Hole Ringdown Signals with Data Gaps using a Deep-Learning Framework introduces DenoiseGapFiller (DGF), a dual-branch encoder–decoder that combines Q-transform-based time–frequency inputs with wavelet tokens through a TimeMixer-augmented Transformer core to impute gaps and denoise ringdown signals. Trained on synthetic ringdown data with gaps up to 20%, DGF achieves a mean waveform mismatch as low as $\mathcal{M}\approx 0.002$ at higher SNR and substantially suppresses broadband noise in the $0.01$–$1$ Hz band, while preserving phase and time–frequency coherence of quasi-normal mode ridges. The work demonstrates improved detection evidence and tighter credible regions for parameter estimation in ringdown spectroscopy, highlighting the method’s potential as a preprocessing step for both space- and ground-based gravitational-wave analyses. Limitations include reliance on Gaussian-noise training and a restricted parameter space; future directions include incorporating real instrumental noise, uncertainty quantification via Bayesian methods, and extensions to multi-mode or multi-detector scenarios to broaden applicability.

Abstract

We introduce DenoiseGapFiller (DGF), a deep-learning framework specifically designed to reconstruct gravitational-wave ringdown signals corrupted by data gaps and instrumental noise. DGF employs a dual-branch encoder-decoder architecture, which is fused via mixing layers and Transformer-style blocks. Trained end-to-end on synthetic ringdown waveforms with gaps up to 20% of the segment length, DGF can achieve a mean waveform mismatch of 0.002. The residual amplitudes of the Time-domain shrink by roughly an order of magnitude and the power spectral density in the 0.01-1 Hz band is suppressed by 1-2 orders of magnitude, restoring the peak of quasi-normal mode(QNM) in the time-frequency representation around 0.01-0.1 Hz. The ability of the model to faithfully reconstruct the original signals, which implies milder penalties in the detection evidence and tighter credible regions for parameter estimation, lay a foundation for the following scientific work.

Figures (12)

• Figure 1: Schematic overview of the pipeline of DGF. The input data with a length of 1056 (noise plus signal with gap) goes through two branches. One branch directly performs q-transform on the data to obtain the amplitude and angle in the time direction and frequency scale, which is used as the first receiver of the dual-channel image format data input into the model, and the other branch normalizes data and performs wavelet transform processing to obtain the data of 8 channels. Finally, the data of each channel is segmented with 50% overlap to obtain a 32-group signal with a length of 64. Each group is regarded as a token input into the second receiver of the model. Output from DGF model is inverse-normalized to obtain the reconstructed waveform.
• Figure 2: Schematic overview of the DGF architecture. The dual-branch encoder receives Q-transform and tokenized wavelet patches in parallel. The embedding module integrates token, convolutional embeddings to encode localized time–frequency features and statistical context. Positional embeddings are added, followed by residual connected 2D convolutions and stacked BiTransformer encoder layers (16 blocks) with multi-head attention to model both short- and long-range dependencies. The decoder contains an MLP layer, followed by reverse token embedding and inverse wavelet transform and 1D convolution to reconstruct the final waveform.
• Figure 3: Histograms of MSE and MAE for the two SNR regimes. Improved amplitude recovery at higher SNR.
• Figure 4: Training (blue) and validation (orange) loss curves for the gap-filling model. Both losses decrease rapidly during the first 10 epochs and then plateau, with validation closely tracking training, indicating good generalization and convergence.
• Figure 5: Qualitative examples of DGF reconstruction on test samples. The green trace is the reconstructed signal, red indicates the gap region, yellow is the noisy input with gap, and blue is the original signal. The sampling frequency is $2\,\mathrm{Hz}$.