A Unified Approach for Simultaneous Graph Learning and Blind Separation of Graph Signal Sources

• Published in: IEEE transactions on signal and information processing over networks 2022-01, Vol.8, p.543-555
• Main Authors: Einizade, Aref, Sardouie, Sepideh Hajipour
• Format: Article
• Language: English
• Subjects: Asymptotic methods; Blind source separation; blind source separation (BSS); Electroencephalography; graph learning (GL); Graph signal processing (GSP); Graphs; Information processing; Machine learning; Matrix decomposition; Noise reduction; Optimization; Separation; Signal processing; Signal processing algorithms; Sparse matrices; Task analysis
• ISSN: 2373-776X; 2373-7778
• DOI: 10.1109/TSIPN.2022.3183498

In the nascent and challenging problem of the blind separation of the sources (BSS) supported by graphs, i.e., graph signals, along with the statistical independence of the sources, additional dependency information can be interpreted from their graph structure. To the best of our knowledge, in these cases, only GraDe and GraphJADE methods have been proposed to exploit the graph dependencies and/or Graph Signal Processing (GSP) techniques to improve the separation quality. Despite the significant advantages of these graph-based methods, they assume that the underlying graphs are known, which is a serious drawback, especially in many real-world applications. To address this issue, in this paper, we propose a Unified objective function for GraphJADE with Graph Learning (GL), namely U-GraphJADE-GL, and use the Block Coordinate Descent (BCD) to optimize it, which along with the separation task, the underlying graphs are learned simultaneously. We compare the performance of the U-GraphJADE-GL with the GraDe with GL (U-GraDe-GL) and the conventional BSS methods in the BSS task and also analyze the GL performance. Besides, as well as the theoretical and experimental convergence analysis, we derive/state the Cramér-Rao bound (CRB) on the estimation of the mixing and unmixing matrices and also on the attainable Interference-to-Source Ratio (ISR), and compare the asymptotic performance of the proposed method with the optimal CRB estimators. To investigate the applicability in real applications, the proposed method is also successfully applied for denoising the epileptic Electroencephalogram (EEG) signals and also for the audio speech source separation task.