Null space component analysis for noisy blind source separation

We propose an approach called the Null Space Component Analysis (NCA) algorithm to solve the noisy blind source separation (BSS) problem. In a set of m linearly independent source signals, each signal is associated with a separating operator that includes the signal in its null space and repels other signals from the space. The signal model induced by the m operators represents the space where each operator separates a single signal from the other signals. 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 sparsitybased approaches, NCA is a deterministic and data-adaptive algorithm that can solve both the under-determined and the over-determined BSS problem. To demonstrate the algorithm’s efficiency, we process several signals, including real-life signals obtained from biomedical systems, and compare the results with those derived by other methods.