Monaural Ica of White Noise Mixtures Is Hard

Separation of monaural linear mixtures of ‘white’ source signals is fundamentally ill-posed. In some situations it is not possible to find the mixing coefficients for the full ‘blind’ problem. If the mixing coefficients are known, the structure of the source prior distribution determines the source reconstruction error. If the prior is strongly multi-modal source reconstruction is possible with low error, while source signals from the typical ‘long tailed’ distributions used in many ICA settings can not be reconstructed. We provide a qualitative discussion of the limits of monaural blind separation of white noise signals and give a set of no go cases, finally, we use a so-called Mean Field approach to derive an algorithm for ICA of noisy monaural mixtures with a bi-modal source prior and demonstrate that low error source reconstructions are possible when the bi-modal source is close to binary. This is the first demonstration of blind source separation in noisy monaural mixtures without invoking temporal correlation information.