Hybrid Joint Diagonalization Algorithms

TL;DR

This paper introduces new hybrid joint diagonalization algorithms combining Givens and hyperbolic rotations, improving performance in high-dimensional non-circular signal analysis tasks like blind source separation.

Contribution

It proposes novel Jacobi-like algorithms for hybrid joint diagonalization considering Hermitian and transpose congruences, enhancing performance over existing methods.

Findings

Algorithms outperform state-of-the-art in high-dimensional cases

Performance gains demonstrated through simulation experiments

Effective in blind separation of non-circular sources

Abstract

This paper deals with a hybrid joint diagonalization (JD) problem considering both Hermitian and transpose congruences. Such problem can be encountered in certain non-circular signal analysis applications including blind source separation. We introduce new Jacobi-like algorithms using Givens or a combination of Givens and hyperbolic rotations. These algorithms are compared with state-of-the-art methods and their performance gain, especially in the high dimensional case, is assessed through simulation experiments including examples related to blind separation of non-circular sources.