A non-orthogonal wavelet transformation for reconstructing gravitational wave signals*

Detections of gravitational-wave signals from compact binary coalescences have enabled us to study extreme astrophysical phenomena and explore fundamental physics. A crucial requisite for these studies is to have accurate signal models with characteristic morphologies, which have been challenging for many decades and are still endeavoring to incorporate important physics. Thereby, morphology-independent methods have been developed for identifying a signal and its reconstruction. The reconstructed signal allows us to test the agreement between the observed signal and the estimated theoretical waveform. These methods model observed signals using a tightest (nearly orthogonal basis) set of wavelets in the frame of continuous wavelet transformation. Here, we propose log-uniform scales to construct the wavelets, which are highly redundant (non-orthogonal) compared to the conventional octave scales but more efficient in reconstructing the signals at high frequencies. We also introduce a semi-model-dependent method for reconstructing the signals using the Gabor-Morlet wavelets with log-uniform scales. We demonstrate the ability to detect deviation using a numerical simulation of eccentric binary black holes merger, where the signal in the data does not belong to the search template waveform manifold. Finally, we apply this method to each binary black hole merger event in GWTC-1. We have found that the signal produced by the GW150914 event and its estimated theoretical waveform has an agreement at ∽ 96% level. As the detector sensitivity improves and the detected population of black hole mergers grows, we expect the proposed method will provide even stronger tests.