From global to local low-rank approximations: Segmentation-based blind source separation for non-stationary source signals

In Blind Source Separation (BSS), we aim to recover source signals from their mixtures without prior knowledge of the mixing process. Applications can be found in various fields such as biomedical signal processing, telecommunications, and array processing. Deterministic tensor-based methods, such as Hankelization, Löwnerization and segmentation, have emerged as alternatives to stochastic approaches such as Independent Component Analysis (ICA). These methods exploit low-rank structures to achieve separation, leveraging the favorable mathematical properties of tensors. Non-stationary source signals, however, can pose challenges for deterministic BSS. Changes in the signal characteristics over time can lead to an increased rank in the low-rank components, reducing the effectiveness of the global low-rank approximation. Addressing this, segmentation-based BSS provides a promising pathway by allowing the signal to be partitioned into locally stationary segments, each of which can be modeled with a lower rank.