Null space component analysis for noisy blind source separation

• A deterministic noisy blind source separation approach is proposed.
• We introduce an adaptive operator to separate one source from the other sources in blind source separation problem.
• We show in theory that our approach can separate linear independent sources.
• The approach can be formulated as a constrained optimization problem with the constraint on the rank of the separating operators.
• Experiments demonstrate that the proposed approach outperforms many other approaches in general.

We propose a novel operator-based model called the null space component analysis (NCA) to solve the noisy blind source separation (BSS) problem. Theoretically, we show that the NCA can resolve the rotation ambiguity in the BSS problem. In a set of m linearly independent source signals, the basic principle of the NCA is to associate each signal with a separating operator that includes the signal in its null space and repels other signals from the space. We show that the model can act as a constraint on the source signals in the noisy BSS problem. In contrast to the ICA-based and the sparsity-based approaches, NCA is a deterministic and data-adaptive algorithm that can solve both the under-determined and the over-determined BSS problems. To demonstrate the algorithm׳s efficiency, we process several types of signals, including real-life signals obtained from biomedical systems, and compare the results with those derived by other methods.