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Your model $\mathbf{x}_n = \mathbf{s}_n + \mathbf{w}_n$ seems too simplistic. It basically says that your output is just some input corrupted by noise. (Unless $\mathbf{s}_n$ is not really your input but some transformed version of it.) Usually, it's more complicated than that in physical systems. This is why a better model would be $\mathbf{x}= \mathbf{... 2 This appears similar to a classic least squared solution of an overdetermined equation that proceeds as follows: Starting with: $$\mathbf{x} = \mathbf{A} \mathbf{s}$$$\mathbf{A}$is not a square matrix if overdetermined (more equations than unknownns) so therefore an inverse does not exist. What you do then is multiply both sides by the transpose of$\...

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Yes and no. The original ICA methods were not made for the case where there is noise on the signal. However, there exist relatively straightforward extensions that work for noisy signals (e.g. [*]). In this case, you can expect some degree of noise suppression but it won't be perfect. That means that ideally, your desired signal components will stick out ...

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In a way, you have answered this already with: FastICA suppose that we have as many sources as channels, but does not check it in any way. If I am going to run the algorithm on my data, it would extract two sources and a 2x2 mixing matrix. ICA will indeed provide a separation, along the lines of section 3 ("What is independence?") which would also ...

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For pre-processing I used EEGLAB, that really help, because EEGLAB have ICA tools for extract Independent Components, that's mean you can check how much of your signals are artifacts (eye moved, blink,muscular moved ), and how much really is brain signal.

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