MaxWave: Rapid maximum likelihood wavelet reconstruction of non-Gaussian features in gravitational wave data

TL;DR

MaxWave delivers a rapid, low-latency approximate maximum-likelihood reconstruction of non-Gaussian features in gravitational-wave data, addressing glitches with real-time, multi-detector capacity. It achieves this through a white wavelet basis with analytic inner products, a TFτ transform that localizes power, and downsampled heterodyned transforms, enabling nonwhitened reconstructions and Fisher-information-based error envelopes. Compared to BayesWave FastStart, MaxWave offers orders-of-magnitude speedups while maintaining competitive reconstruction quality, and its refined solutions approach BayesWave RJMCMC performance at higher SNR and larger mass-ratio transients. These advances enable rapid glitch identification, extended training data for ML classifiers, and potential integration into low-latency, multi-detector burst searches and LVK analyses.

Abstract

Advancements in the sensitivity of gravitational wave detectors have increased the detection rate of transient astrophysical signals. We improve the existing BayesWave initialization algorithm and present a rapid, low latency approximate maximum likelihood solution for reconstructing non-Gaussian features. We include three enhancements: (1) using a modified wavelet basis to eliminate redundant inner product calculations; (2) shifting from traditional time-frequency-quality factor wavelet transforms to time-frequency-time extent transforms to optimize wavelet subtractions; and (3) implementing a downsampled heterodyned wavelet transform to accelerate initial calculations. Our model can be used to denoise long-duration signals, which include the stochastic gravitational wave background from numerous unresolved sources and continuous wave signals from isolated sources such as rotating neutron stars. Through our model, we can also supplement machine learning applications that use spectrographic training data to classify and understand glitches by providing nonwhitened, time and frequency domain reconstructions of any glitch.

Figures (11)

• Figure 1: Traditional model Neil-BWstart-2021 for reconstructing noise transients using an approximate, iterative maximum likelihood solution. This model has several limitations including the costs of calculating the original wavelet transform using an overcomplete basis, recomputing noise-weighted inner products for updated TFQ wavelet transforms after each subtraction, and subtracting a large number of pixels as power heavily smears across different Q layers. The computational bottlenecks of the algorithm are highlighted in shades of red.
• Figure 2: Modified model for constructing the approximate, iterative maximum likelihood solution. The computational cost of the original wavelet transform is reduced by base-banding whitened data and using downsampled heterodyned calculations. The hefty cost of recomputing TF$\tau$ transforms after each subtraction is entirely avoided by shifting to analytic wavelet inner products using white wavelets. The number of iterations or pixel subtractions required is also significantly reduced for the TF$\tau$ maps as the power of the brightest wavelet is well-localized in all the $\tau$ layers. Wavelet parameters retrieved can be used to reconstruct the signal corresponding to the approximate maximum likelihood solution.
• Figure 3: A single Morlet-Gabor wavelet in the original (gray waveform) and white basis (blue waveform) is plotted at the top. The bottom plot shows the gravitational wave signal GW150914 GW150914GWTC-1GWOSC_O1_O3 reconstruction using the original (gray waveform) and white (blue waveform) wavelet basis. Wavelets from the original basis are smooth in the whitened domain, whereas white wavelets show small-scale variations due to the whitening filter. However, we can use the $t_0, f_0$, and $\tau$ pixels from analytical subtractions in the white wavelet basis to reconstruct a physical signal in the original basis, and then compute the approximate maximum likelihood solution.
• Figure 4: TF$\tau$ map for GW150914 signal GW150914GWTC-1GWOSC_O1_O3 in the LIGO Hanford detector calculated using wavelet transforms in the nonorthogonal, overcomplete, white wavelet basis. Each $\tau$ layer has a different time and frequency resolution. Pixel darkness is proportional to the signal-to-noise ratio of the signal. We boost the wavelet transform using $\tau$ dependent downsampling and heterodyned calculations that base-band segments of the whitened data and interpolate it with wavelets at a fixed low frequency.
• Figure 5: False detection rate for MaxWave recovery of ten-thousand, 4 second long Gaussian noise realizations. The histogram shows number of detections (first column) and the number of wavelets recovered (subsequent columns) as a fraction of the number of noise realizations. The false detection rate is less than 1 %. Also note that we intentionally suppress the detection of a single wavelet (second column) since glitches and signals are better modeled as clustered power.