Robust blind separation of sparse sources based on morphological diversity and low-rank matrix recovery

This paper presents a robust blind separation method of sparse sources named robust sparse blind source separation (r-SBSS). Allowing for the morphological diversity of the source, we first assume that one source can be divide into two parts, namely global component and local component. Furthermore, a novel optimization model is built upon the low-rank matrix recovery and the sparse modeling of both the sources and the outliers with different regularized constraints. We also provide the corresponding optimization algorithm, which allows combining both low-rank double dictionary learning and low-rank representation strategy to realize source separation and mixing matrix estimation respectively. In the proposed method, the dictionary learning strategy guarantees the adaptive representation of sparsity, and the low-rank representation strategy is first introduced to implement the effective estimation of the mixing matrix and outliers. Extensive experimental results on AR dataset and real EMI signals demonstrate the superiority of r-SBSS, compared to the state-of-the-art methods.