A Tensor-Based Method for Large-Scale Blind Source Separation Using Segmentation

Many real-life signals are compressible, meaning that they depend on much fewer parameters than their sample size. In this paper, we use low-rank matrix or tensor representations for signal compression. We propose a new deterministic method for blind source separation that exploits the low-rank structure, enabling a unique separation of the source signals and providing a way to cope with large-scale data. We explain that our method reformulates the blind source separation problem as the computation of a tensor decomposition, after reshaping the observed data matrix into a tensor. This deterministic tensorization technique is called segmentation and is closely related to Hankel-based tensorization. We apply the same strategy to the mixing coefficients of the blind source separation problem, as in many large-scale applications, the mixture is also compressible because of many closely located sensors. Moreover, we combine both strategies, resulting in a general technique that allows us to exploit the underlying compactness of the sources and the mixture simultaneously. We illustrate the techniques for fetal electrocardiogram extraction and direction-of-arrival estimation in large-scale antenna arrays.