Wavescan: multiresolution regression of gravitational-wave data

Identification of a transient gravitational-wave signal embedded into non-stationary noise requires the analysis of time-dependent spectral components in the resulting time series. The time-frequency distribution of the signal power can be estimated with Gabor atoms, or wavelets, localized in time and frequency by a window function. Such analysis is limited by the Heisenberg-Gabor uncertainty, which does not allow a high-resolution localization of power with individual wavelets simultaneously in time and frequency. As a result, the temporal and spectral leakage affects the time-frequency distribution, limiting the identification of sharp features in the power spectrum. This paper presents a time-frequency regression method where instead of a single window, a stack of wavelets with different windows spanning a wide range of resolutions is used to scan power at each time-frequency location. Such a wavelet scan (dubbed in the paper as wavescan) extends the conventional multiresolution analysis to capture transient signals and remove the local power variations due to the temporal and spectral leakage. A wavelet, least affected by the leakage, is selected from the stack at each time-frequency location to obtain the high-resolution localization of power. The paper presents all stages of the multiresolution wavescan regression, including the estimation of the time-varying spectrum, identification of transient signals in the time-frequency domain, and reconstruction of the corresponding time-domain waveforms. To demonstrate the performance of the method, the wavescan regression is applied to the gravitational wave data from the LIGO detectors.