Hierarchical Probabilistic Model for Blind Source Separation via Legendre Transformation

TL;DR

This paper introduces IGBSS, a hierarchical probabilistic model for blind source separation that leverages information geometry and Legendre transformation to improve signal recovery.

Contribution

It proposes a novel hierarchical log-linear model with theoretical guarantees for unique source signal recovery in blind source separation.

Findings

Outperforms established techniques on images and time series data.

Successfully separates signals with complex interactions.

Provides theoretical guarantees for signal recovery.

Abstract

We present a novel blind source separation (BSS) method, called information geometric blind source separation (IGBSS). Our formulation is based on the log-linear model equipped with a hierarchically structured sample space, which has theoretical guarantees to uniquely recover a set of source signals by minimizing the KL divergence from a set of mixed signals. Source signals, received signals, and mixing matrices are realized as different layers in our hierarchical sample space. Our empirical results have demonstrated on images and time series data that our approach is superior to well established techniques and is able to separate signals with complex interactions.