SSS: Separation of Synchronous Sources
The problem of separating synchronous sources (SSS) is a case of blind source separation (BSS) where independence of the sources is not satisfied. In SSS, the sources are assumed to be complex-valued, and different sources are phase-locked, which means that the relative phase lag between two sources is not uniform in [0,2*pi[. For this reason, the typical independent component analysis (ICA) tools are theoretically not applicable, and experiments show that they perform poorly in this task. In the SSS model, we assume that the phase lag between any two sources is constant. The only important assumption regarding the amplitudes of the sources is linear independence, although some nice results can be proven if the amplitudes are statistically independent.
In this talk, I’ll start by briefly discussing ICA, since it is relatively familiar in the Machine Learning community. I will then formulate the problem of SSS and detail the similarities and differences to the ICA problem. Afterwards, I will present two algorithms that were developed to tackle this problem, along with some nice theoretical properties of those algorithms. We will visit some very simple optimization problems and a little bit of complex algebra.
Nothing complicated, I promise!
I will finalize by presenting some simulated results, on 1) data which exactly follows the SSS model, and 2) data which deviates from the SSS model.