Statistical complexity as a criterion for the useful signal detection problem

TL;DR

This paper evaluates three variants of statistical complexity functions for detecting useful signals within noisy data, analytically deriving their maximum distributions and proposing a threshold selection method, with total variation complexity showing superior detection performance.

Contribution

It introduces and compares three variants of statistical complexity for signal detection, providing analytical maximum distributions and a threshold selection method.

Findings

Total variation complexity outperforms other variants in detection accuracy.

Analytical maximum distributions for each complexity variant are derived.

A threshold selection method based on maximum complexity values is proposed.

Abstract

Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants of statistical complexity are obtained analytically and conclusions about the efficiency of using one or another variant for detection problem are made. The comparison of considered information characteristics is shown and analytical results are illustrated on an example of synthesized signals. A method is proposed for selecting the threshold of the information criterion, which can be used in decision rule for useful signal detection in the signal-noise mixture. The choice of the threshold depends a priori on the analytically obtained maximum values. As a result, the complexity based on the total variation demonstrates the best ability of useful signal detection.