Semi-blind Source Separation via Sparse Representations and Online Dictionary Learning

This work examines a semi-blind single-channel source separation problem. Our specific aim is to separate one source whose local structure is approximately known, from another a priori unspecified background source, given only a single linear combination of the two sources. We propose a separation technique based on local sparse approximations along the lines of recent efforts in sparse representations and dictionary learning. A key feature of our procedure is the online learning of dictionaries (using only the data itself) to sparsely model the background source, which facilitates its separation from the partially-known source. Our approach is applicable to source separation problems in various application domains; here, we demonstrate the performance of our proposed approach via simulation on a stylized audio source separation task.

💡 Research Summary

The paper tackles a semi‑blind single‑channel source separation problem in which one component (the “target” source) possesses a partially known local structure, while the other component (the “background” source) is completely unspecified. Unlike fully blind source separation, which relies on statistical independence or other strong assumptions for all sources, the semi‑blind setting exploits a modest amount of prior knowledge about the target source to improve separation quality.
The authors formulate the observed mixture (x\in\mathbb{R}^N) as the sum of two latent signals:
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