Separation of speech from multiple speakers speaking in different microphones connected to a mixer
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From: markt on 7 May 2008 12:12 >>C) "Most ICA methods are not able to extract the actual number of >> source signals, the order of the source signals, nor the signs >> or the scales of the sources." >> >>Contemplate that one for a bit, particularly in view of >>quote A) at the top: "Most" ICA methods can't do the job >>ICA is supposed to do! Mind you, in line with the great >>academic tradition, the word 'most' is here used in one >>of two functions: > >The first part of this is a bit nebulous since there is a point at which >some sources are simply lost in the background. You have to have some a >priori guess with any blind detection method as to how large your spread >is, e.g., you sort of need to know how large your delay spread in a comm >channel is before deciding how many multipaths there actually are. I should add, the "nebulous" part of the statement is that you have to run ICA repeatedly until you get to a point you think you have resolved all of the individual sources. This requires either a priori information (as I mentioned) about the number of sources, e.g., you know there are 10 sources so you find 10 independent results and quit, or some criteria to test each output. For speech, the test could be something like checking for an intelligible output, or perhaps that the output signals actually contain formants that resemble speech. Both would require a pattern matching algorithm of sorts, as I see it, on the output. Since PCA is variance-based, you can collect enough vectors that describe some pre-determined amount of the total signal variance, say 95%, and assume the rest is either unrecoverable or noise. Mark
From: markt on 7 May 2008 13:26
>I don't buy that, unless you come up with an anal definition >of the problem ICA is supposed to solve. My experience is >with Direction of Arrival problems which aims at separating >multiple sources in a spatial domain. MUSIC is a very popular >choise as basis for investigations, and in that case it is >a trivial excercise to show that the maxmum number of sources >is strongly related to the number of sensors in the array. I made it pretty clear that with a single receiver you lose spatial resolution, i.e., you no longer have DOA information. I'm not talking about exploiting DOA, but independence. An MMSE receiver for a comm system, for example, exploits the fact that users/multipaths are uncorrelated. You start with an input signal, r, and your symbol length, M, as well as delay spread, P. You collect a vector r_vec(n) = [r(n+M+P-1) r(n+M+P-2) ... r(n)]^T, which gives you M+P "observations" used to estimate the channel impulse response. The MMSE result is given by the solution to the Wiener-Hopf equation w = inv(R)*p where R is E{r_vec*r_vec^H} and p is E{r*conj(r_vec)}; >The reason is that MUSIC and similar methods is based on >examining certain eigenvectors of the signal covariance >matrix. The dimension of that covariance matrix is given >by the number of sensors, which in turn govern the whole >analysis. I would be cerys surprised if the analysis of >ICA is fundamentally different. Depends upon how you implement it. All ICA does (essentially) is use higher-order statistics. Nothing magical, just an extension of the fact that if you have a linear combination of independent vectors, there is only one solution that results in independent vector outputs. If you have multiple receivers, you also have DOA information which can only help. >I have expereience with multipath in sonar environments. >There is nothing available which comes even remotely >close to work 'quite well' in multipath scenarios. I'm sorry to hear that. Comm systems (DS-CDMA) employ a RAKE on the forward link which is typically implemented with a bank of correlator receivers to estimate each of the multipaths. Of course, you have the pilot sequence, which is known, to base your estimation on. The correlator receiver is not optimal (w.r.t. MSE) in the presence of multipath or anything other than an AWGN channel. The MMSE receiver above, is, however, and knowledge of the pilot is unnecessary. I suspect, perhaps, that the delay spread in sonar is very large? That might make a solution in that realm very difficult. >I don't trust the details supplied by a method which misses >a main parameter like the number of sources present. Well, it is "blind," so this is hardly a surprise. That's why there's research in the area, because applications in which a priori information is not available are more common than not. I also pointed out that PCA provides a means for determining the number of sources, which is typically applied on the front-end of an ICA system. For example, besides pre-whitening, you could examine the autocorrelation matrix and come to conclusions about the number of sources present. There is no one method that's going to universally solve all of these (and other) problems. >So you don't learn anything new from that sort of analysis, >but rather get your prejudice confirmed? If you need to >'guess' or 'assume' major parameters of the scenario you >have already lost. If you use a deterministic parametric >model you state your assumptions clearly up front and is >able to analyze them, and also have a fair chance of >spotting flaws when such occur. "Blind" methods hides >such factors from the analysi, obfuscating the whole >picture. I'm not sure what you're getting at here. ICA will separate the sources if they are independent (or nearly so). Couple the ICA with other methods (PCA) and you have good estimates of the parameters you request. The real-world isn't so kind as to provide all the answers automatically. The whole purpose of blind methods is exactly to deal with scenarios in which you do not have complete information. The reverse link of a comm system has to guess how many users are present before they are acquired. There is no deterministic way to make this assumption a priori, yet my cell phone works quite well (most of the time). How is this any different? Mark |