Efficiently enclosing the compact binary parameter space by singular-value decomposition

TL;DR

This paper demonstrates that singular value decomposition can efficiently reduce the number of filters needed in gravitational-wave searches, and that a low-density basis can accurately represent denser template banks, with potential applications in waveform interpolation.

Contribution

It shows how SVD basis sets from low-density banks can accurately reconstruct denser template banks in gravitational-wave data analysis.

Findings

SVD basis reduces filter count in searches.

Low-density SVD basis can reconstruct dense banks.

Potential for interpolating numerical relativity waveforms.

Abstract

Gravitational-wave searches for the merger of compact binaries use matched-filtering as the method of detecting signals and estimating parameters. Such searches construct a fine mesh of filters covering a signal parameter space at high density. Previously it has been shown that singular value decomposition can reduce the effective number of filters required to search the data. Here we study how the basis provided by the singular value decomposition changes dimension as a function of template bank density. We will demonstrate that it is sufficient to use the basis provided by the singular value decomposition of a low density bank to accurately reconstruct arbitrary points within the boundaries of the template bank. Since this technique is purely numerical it may have applications to interpolating the space of numerical relativity waveforms.