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978-3-8439-1121-4, Reihe Informationstechnik
Complex Blind Source Separation with Audio Applications
237 Seiten, Dissertation Universität Stuttgart (2013), Softcover, A5
This PhD thesis studies blind source separation of complex signals and applies it to the separation of audio mixtures. In the simplest signal model, we can observe noiseless linear combinations of unobservable original signals. The task is to reconstruct the original signals without knowledge of the mixing coefficients. Blind source separation is a versatile approach since the physical phenomenon underlying the mixing process does not need to be modelled. It can hence be applied in various fields such as audio signal processing, telecommunication or medical signal processing.
In this work, we consider separation of complex signals since they often occur in practical problems, e.g. in telecommunication or after a transformation of time-domain signals into the frequency domain. One of the most important approaches for blind source separation is independent component analysis (ICA), which assumes the sources to be statistically independent. A second class of methods uses the fact, that many signals are sparse in the time-frequency domain.
In this thesis, we derive the theoretical limits of linear ICA with respect to variance and bias of estimating the inverse mixing matrix for a general, noncircular complex and instantaneous mixing model. First, we derive the Cramér-Rao bound for noiseless complex ICA. It allows an evaluation of existing ICA algorithms with respect to the achievable performance. Afterwards, we study the bias of the estimated demixing matrix from the inverse mixing matrix for a noisy mixing model. The derivation shows that in many cases the demixing matrix estimated by ICA performs similarly to the linear MMSE estimator which achieves the best signal-to-interference-plus-noise ratio among all linear estimators.
In a second part, we discuss specific aspects of audio source separation, such as convolutive and time-varying mixing, unknown source number, broadband nature of audio signals, as well as the so-called permutation problem of separation approaches in the time-frequency domain. We provide solutions to these different aspects for both ICA and TF sparseness based separation.
Finally, we consider further aspects relevant for applying source separation in practical scenarios and present our prototype system based on frequency-domain ICA and the robust permutation correction method studied in this thesis. It allows realtime separation with a very low input-output delay and can hence be used in time-critical applications.