Riemannian geometry for Compound Gaussian distributions: application to recursive change detection

TL;DR

This paper introduces a Riemannian geometric framework for Compound Gaussian distributions, enabling efficient recursive change detection in multivariate image time series with improved performance.

Contribution

It develops a novel Riemannian geometry for Compound Gaussian distributions, including Fisher information metric, geodesics, and distance, applied to recursive change detection.

Findings

Achieves optimal change detection performance on simulated data.

Offers computational efficiency over existing methods.

Provides a new geometric approach for statistical modeling.

Abstract

A new Riemannian geometry for the Compound Gaussian distribution is proposed. In particular, the Fisher information metric is obtained, along with corresponding geodesics and distance function. This new geometry is applied on a change detection problem on Multivariate Image Times Series: a recursive approach based on Riemannian optimization is developed. As shown on simulated data, it allows to reach optimal performance while being computationally more efficient.