Abstract

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.

Code description

This package provides experiment files and auxiliary files for the segmentation-based blind source separation paper.

Reference

M. Boussé, O. Debals, L. De Lathauwer, "A tensor-based method for large-scale blind source separation using segmentation," IEEE Transactions on Signal Processing, vol. 62, no. 2, pp. 346-358, Jan. 2017.

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