# Reconstructing Gravitational Wave Core-Collapse Supernova Signals with Dynamic Time Warping

## TL;DR

This paper introduces a method combining principal component analysis with dynamic time warping to improve the reconstruction of gravitational wave signals from core-collapse supernovae, especially for longer and complex waveforms.

## Contribution

The study demonstrates that integrating DTW with PCA enhances waveform reconstruction accuracy and reduces the number of components needed, addressing limitations of previous PCA-based methods.

## Key findings

- DTW reduces the number of PCs needed from nine to four for 90% data representation.
- Reconstruction match improves at SNRs between 0 and 50.
- Method effectively reconstructs longer, complex CCSN waveforms.

## Abstract

Core-collapse supernovae (CCSNe) are a potential source for ground-based gravitational wave detectors, as their predicted emission peaks in the detectors' frequency band. Typical searches for gravitational wave bursts reconstruct signals using wavelets. However, as CCSN signals contain multiple complex features in the time-frequency domain, these techniques often struggle to reconstruct the entire signal. An alternative method developed in recent years involves applying principal component analysis (PCA) to a set of simulated CCSN models. This technique enables model selection between astrophysical CCSN models as well as waveform reconstruction. However, PCA faces its own difficulties, such as being unable to reconstruct signals longer than the simulations; many CCSN simulations are stopped before the emission peaks due to insufficient computational resources. In this study, we show how combining PCA with dynamic time warping (DTW) improves the reconstruction of CCSN gravitational wave signals in Gaussian noise characteristic of Advanced LIGO at design sensitivity. For the waveforms used in this analysis, we find that the number of PCs needed to represent 90% of the data is reduced from nine to four by applying DTW, and that the match between the original and reconstructed waveforms improves for signal-to-noise ratios in the range [0,50].