Robust Blind Source Separation by Soft Decision-Directed Non-Unitary Joint Diagonalization

TL;DR

This paper introduces a robust method for non-unitary joint diagonalization that effectively reduces the impact of outliers, improving convergence and accuracy in statistical signal processing applications.

Contribution

It proposes a novel cost function with a soft decision-directed scheme and an efficient algorithm for non-unitary joint diagonalization that enhances robustness against outliers.

Findings

Outperforms conventional algorithms in convergence speed.

Demonstrates increased robustness to outliers.

Achieves better accuracy in estimating the mixing matrix.

Abstract

Approximate joint diagonalization of a set of matrices provides a powerful framework for numerous statistical signal processing applications. For non-unitary joint diagonalization (NUJD) based on the least-squares (LS) criterion, outliers, also referred to as anomaly or discordant observations, have a negative influence on the performance, since squaring the residuals magnifies the effects of them. To solve this problem, we propose a novel cost function that incorporates the soft decision-directed scheme into the least-squares algorithm and develops an efficient algorithm. The influence of the outliers is mitigated by applying decision-directed weights which are associated with the residual error at each iterative step. Specifically, the mixing matrix is estimated by a modified stationary point method, in which the updating direction is determined based on the linear approximation to the gradient function. Simulation results demonstrate that the proposed algorithm outperforms conventional non-unitary diagonalization algorithms in terms of both convergence performance and robustness to outliers.