MaxWave: Rapid Maximum Likelihood Wavelet Reconstruction of Non-Gaussian features in Gravitational Wave Data

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 (TFQ) wavelet transforms to time-frequency-time extent (TF$\tau$) transforms to optimize wavelet subtractions; and (3) implementing a downsampled heterodyned wavelet transform to accelerate initial calculations. Our model can be used to de-noise 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 aid machine learning applications that aim to classify and understand glitches by providing non-whitened, time and frequency domain, Gaussian-noise-free reconstructions of any glitch.