Adaptive multiresolution for wavelet analysis

TL;DR

This paper introduces an adaptive wavelet packet decomposition method that automatically selects optimal time-frequency resolution for gravitational wave detection, improving signal analysis and reducing false alarms.

Contribution

It proposes a novel adaptive wavelet decomposition technique based on entropy minimization, enhancing analysis of unknown signal shapes in gravitational wave data.

Findings

Reduces false alarm rate in burst detection

Maintains high detection efficiency

Provides clearer time-frequency scalograms

Abstract

We present a new method of wavelet packet decomposition to be used in gravitational wave detection. An issue in wavelet analysis is what is the time-frequency resolution which is best suited to analyze data when in quest of a signal of unknown shape, like a burst. In the other wavelet methods currently employed, like LIGO WaveBurst, the analysis is performed at some trial resolutions. We propose a decomposition which automatically selects at any frequency the best resolution. The criterion for resolution selection is based on minimization of a function of the data, named entropy in analogy with the information theory. As a qualitative application we show how a multiresolution time-frequency scalogram looks in the case of a sample signal injected over Gaussian noise. For a more quantitative application of the method we tested its efficiency as a non-linear filter of simulated data for burst searches, finding that it is able to lower the false alarm rate of the WaveBurst algorithm with negligible effects on the efficiency.