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How to recover uncorrelated N sources from given N-1 signals and known mixing matrix M, (e.g. 9x8 matrix)?

If I just use pseudo-inverse matrix M+, my source estimates are correlated with each other in the way that each i'th estimate S* equals:

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Correlation arises from that sum of all sources S, present in every estimate S*. How can I get uncorrelated source estimates?

From this formulae, using preudo-inverse mixing matrix is correct, only when sum of all sources S equals to zero ("zero signal").

So, I suppose that I should find some other missing mixing weights for "zero signal", such that decorrelate my source estimates. How to do it?

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