Generalized Non-orthogonal Joint Diagonalization with LU Decomposition and Successive Rotations
This work addresses a specific bottleneck in joint blind source separation for signal processing applications, representing an incremental advancement over existing methods.
The paper tackled the problem of handling multiple datasets with inter-set dependencies in joint blind source separation by proposing a generalized non-orthogonal joint diagonalization algorithm using LU decomposition and successive rotations, achieving performance improvements as demonstrated in experiments with synthetic and real-world datasets.
Non-orthogonal joint diagonalization (NJD) free of prewhitening has been widely studied in the context of blind source separation (BSS) and array signal processing, etc. However, NJD is used to retrieve the jointly diagonalizable structure for a single set of target matrices which are mostly formulized with a single dataset, and thus is insufficient to handle multiple datasets with inter-set dependences, a scenario often encountered in joint BSS (J-BSS) applications. As such, we present a generalized NJD (GNJD) algorithm to simultaneously perform asymmetric NJD upon multiple sets of target matrices with mutually linked loading matrices, by using LU decomposition and successive rotations, to enable J-BSS over multiple datasets with indication/exploitation of their mutual dependences. Experiments with synthetic and real-world datasets are provided to illustrate the performance of the proposed algorithm.