Probabilistic Blind Source Separation

Rasmus Kongsgaard Olsson

AbstractThis thesis focuses on Blind source separation (BSS), which is the problem of finding hidden source signals in observed mixtures given no or little knowledge about the sources and the mixtures. Based on the well-performing, yet heuristically based, algorithm of Parra and Spence, 2000, a probabilistic model is formulated for the BSS problem. A time-domain EM algorithm KaBSS is derived which estimates the source signals, the associated second-order statistics, the mixing filters and the observation noise covariance matrix. In line with the literature, it is found that the estimated quantities are unique within the model only if the sources can be assumed non-stationary and contain sufficient time-variation. Furthermore, the statistical framework is exploited in order to assess the correct model order: the number of sources within the mixture can be determined using the socalled Bayes Information Criterion (BIC). Monte Carlo simulations as well as experimental results for mixtures of speech signals are documented and compared to results obtained by the algorithm of Parra and Spence.

In Danish:

Denne afhandlings emne er blind signalseparation (BSS), der drejer sig om at estimere skjulte kildesignaler i observerede blandinger på basis af ringe eller ingen viden om kildesignaler og blandinger. En probabilistisk model for BSS-problemet formuleres med afsæt i Parra og Spences (2000) højtydende, men heuristisk funderede algoritme. På baggrund af modellen udledes KaBSS , en EM-algoritme, der estimerer kildesignalerne og deres 2. ordensstatistik, blandingsfiltrene og observationsstøjens kovarians. I overensstemmelse med litteraturen findes det, at de estimerede størrelser kun er unikke indenfor modellen, hvis en antagelse om kildernes ikke-stationaritet er rimelig, og hvis kilderne er tilstrækkelig tidsvariante. Ydermere udnyttes den statistiske ramme til at vurdere den korrekte modelorden: Antallet af kilder i blandingen fastslås ved at benytte det såkaldte Bayes Information Criterion (BIC). Såvel Monte Carlo simulationer som eksperimentelle resultater for blandinger af talesignaler dokumenteres og sammenlignes med resultater, opn°aet via Parra og Spences algoritme.
KeywordsBlind source separation, Independent component analysis, non-stationary sources, EM
TypeMaster's thesis [Academic thesis]
Year2004
PublisherInformatics and Mathematical Modelling, Technical University of Denmark, DTU
AddressRichard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby
SeriesIMM-Thesis-2004-7
NoteSupervised by Professor Lars Kai Hansen
Electronic version(s)[pdf] [ps]
BibTeX data [bibtex]
IMM Group(s)Intelligent Signal Processing


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