?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Source+Separation+in+the+Presence+of+Side+Information%3A+Necessary+and+Sufficient+Conditions+for+Reliable+De-Mixing&rft.creator=Sabetsarvestani%2C+Z&rft.creator=Renna%2C+F&rft.creator=Kiraly%2C+F&rft.creator=Rodrigues%2C+MRD&rft.description=This+paper+puts+forth+new+recovery+guarantees+for+the+source+separation+problem+in+the+presence+of+side+information%2C+where+one+observes+the+linear+superposition+of+two+source+signals+plus+two+additional+signals+that+are+correlated+with+the+mixed+ones.+By+positing+that+the+individual+components+of+the+mixed+signals+as+well+as+the+corresponding+side+information+signals+follow+a+joint+Gaussian+mixture+model%2C+we+characterise+necessary+and+sufficient+conditions+for+reliable+separation+in+the+asymptotic+regime+of+low-noise+as+a+function+of+the+geometry+of+the+underlying+signals+and+their+interaction.+In+particular%2C+we+show+that+if+the+subspaces+spanned+by+the+innovation+components+of+the+source+signals+with+respect+to+the+side+information+signals+have+zero+intersection%2C+provided+that+we+observe+a+certain+number+of+measurements+from+the+mixture%2C+then+we+can+reliably+separate+the+sources%2C+otherwise+we+cannot.+We+also+provide+a+number+of+numerical+results+on+synthetic+data+that+validate+our+theoretical+findings.&rft.subject=Source+separation%2C+Reliability+theory%2C+Atmospheric+measurements%2C+Particle+measurements%2C+Pollution+measurement%2C+Covariance+matrices&rft.publisher=IEEE&rft.date=2019-02-21&rft.type=Proceedings+paper&rft.publisher=IEEE+Global+Conference+on+Signal+and+Information+Processing+(GlobalSIP)&rft.language=eng&rft.source=+++++In%3A++Proceedings+of+the+2018+IEEE+Global+Conference+on+Signal+and+Information+Processing+(GlobalSIP).++(pp.+pp.+351-355).++IEEE%3A+Danvers+(MA)%2C+USA.+(2019)+++++&rft.format=text&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10073199%2F7%2FRodrigues_Source%2520Separation%2520in%2520the%2520Presence%2520of%2520Side%2520Information.%2520Necessary%2520and%2520Sufficient%2520Conditions%2520for%2520Reliable%2520De-Mixing_AAM.pdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10073199%2F&rft.rights=open