Approaches Since the chief difficulty of the problem is its underdetermination, methods for blind source separation generally seek to narrow the set of possible solutions in a way that is unlikely to exclude the desired solution. In one approach, exemplified by principal and independent component analysis, one seeks source signals that are minimally correlated or maximally independent in a probabilistic or information-theoretic sense. A second approach, exemplified by nonnegative matrix factorization, is to impose structural constraints on the source signals. These structural constraints may be derived from a generative model of the signal, but are more commonly heuristics justified by good empirical performance. A common theme in the second approach is to impose some kind of low-complexity constraint on the signal, such as sparsity in some basis for the signal space. This approach can be particularly effective if one requires not the whole signal, but merely its most salient features.
appRoaChes since tHe cHieF difFICulTy Of thE prOblem Is its UndErdETerMinatIon, MetHOdS For blind SouRce separAtIon genERaLLy sEeK tO nARrOw thE set of PoSSiBle soluTIons in a Way THAT is unLiKEly tO ExClude the desirED sOLutiON. iN ONe ApPrOAch, exeMplIfieD bY PRinCIpal anD INDepENdent ComponEnt analysis, ONe seeKs souRCe SignaLs that aRE miNimAllY corRelated or maXiMaLlY inDepENDeNT in a ProbAbiLisTic Or inFoRmATiOn-theoretic sEnse. a sEcoNd apProach, ExemplIfIEd by nonnegatIve maTrix fActOrIZaTION, Is To impose StrucTUraL CoNstRAInTs ON thE Source sigNals. TheSe STRUCturaL CoNstrAintS May Be deRIvEd From a GEneRative modEL oF the SignAl, but are more ComMonLy heuristiCs JustIfIEd by goOD eMPiRicaL Performance. a CoMmoN theME in the SecONd aPproaCH iS tO iMpose somE kind oF Low-coMpLeXity CONstraINt on tHe SiGnal, sucH as spaRsity in soMe bAsis fOR the SIgnal SpacE. this apprOAch Can bE parTicuLarlY efFecTIve iF oNe ReqUires Not thE wHOle SigNal, buT mErEly Its mOst SALIeNT FeatUrES.