The effect of source sparsity on independent vector analysis for blind source separation

In this paper, the effect of source sparsity on the performance of the independent vector analysis (IVA) algorithm for blind source separation is investigated. The IVA algorithm was originally developed under the assumption of statistical independence between the sources and has made great advances in recent years. However, its performance under different sparsity conditions is rarely studied. This study begins by mathematically analyzing the performance of IVA in permutation alignment, which is proved to directly correlate with the degree of frame-level W-disjoint orthogonality (F-WDO) of the sources. We further prove that IVA can theoretically achieve the optimal separation in the cases where the sources are F-WDO. Experimental results show a strong positive correlation between a quantitative measure of F-WDO and the IVA algorithm's performance under various conditions.