Transcription of Blind Source Separation: PCA & ICA - mit.edu
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Blind Source Separation: PCA & ICA - mit.edu
D. Clifford gari [at] mit . ~gari G. D. Clifford 2005-2009 Blind Source Separation: PCA & ICAWhat is BSS?Assume an observation (signal) is a linear mix of >1 unknown independentsource signalsThe mixing (not the signals) is stationaryWe have as manyobservations as unknown sources To find sources in observations- need to define a suitable measure of For example - the cocktail party problem(sources are speakers and background noise):The cocktail party problem - find ZAz1z2zNXTZTXT=AZTx1x2xN2 Formal statement of problem N independentsources ..Zmn( MxN) linear square mixing ..Ann( NxN) (#sources=#sensors) produces a set of observations ..Xmn( MxN).. XT= AZTF ormal statement of solution demix observations ..XT( NxM)into YT= WXTYT(NxM) ZTW(NxN) A-1 How do we recover the independent sources? (We are trying to estimate W A-1).. We require a measure of independence! Signal Source Noise sourcesObserved mixturesZTXT=AZTYT=WXT3XT = A ZTYT = W XTTTTTThe Fourier Transform(Independence between components is assumed) Recap: Non-causal Wiener filteringx[n] - observationy[n] - ideal signald[n] - noise componentIdeal Signal Sy(f)Noise Power Sd(f)Observation Sx(f)Filtered signal: Sfilt(f ) = Sx(f).
4 BSS is a transform? • Like Fourier, we decompose into components by transforming the observations into another vector space which maximises the separation between ...
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