Gradient Flow Independent Component Analysis
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1 Graden Fow Independen Componen Anay Mun Sanaćevć and Ger Cauwenbergh Adapve Mcroyem ab John Hopkn Unvery
2 Oune Bnd Sgna Separaon and ocazaon Prncpe of Graden Fow : from deay o empora dervave Equvaen ac near ICA probem Expermena eparaon reu Spary Independence of graden obervaon Monaura ource eparaon Concuon
3 Bnd Separaon and ocazaon Modeng Source gna propagae a raveng wave n free pace Spaay dvere enor array receve near mxure of medeayed ource The me deay deermne he drecon coordnae of he wave reave o he enor geomery Mehod Super-reouon echnque emae he me deay n he pecra doman, aumng narrowband ource Jon emaon of mupe broadband ource and her me deay pobe n an exended ICA framework, bu requre non-convex opmzaon eadng o unpredcabe performance
4 ( Tempora Sere Expanon + τ ( r)) = ( + τ ( r) & ( + τ ( r) && ( + K deay 0 h -order -order nd -order 3 rd -order 4 h -order Reduce he probem of denfyng me deayed ource mxure o ha of eparang ac mxure of he me-dfferenaed ource Impe ubwaveengh geomery of he enor array
5 Graden Fow Prncpe τ ( + τ ) ξ 0 τ ξ 0 ξ & 00 τ &( τ ( d d [ ] τ τ - ξ& ξ ξ & ( τ & ( τ & ( Graden fow bearng reouon fundamenay ndependen of aperure Reouon deermned by envy of graden acquon Mechanca dfferena coupng (Me e a.) Opca dfferena coupng (Degerekn) Anaog VSI dfferena coupng
6 Separaon and ocazaon Source mxure are oberved wh addve enor noe: Graden fow reduce o a ac (noy) mxure probem: oved by mean of near ac ICA ) ( ) ( ) ( n x pq pq pq + + = = τ n A x + = + = ) ( ) ( ν ν ν τ τ τ τ ξ ξ ξ & & M & & drecon vecor ource (me-dfferenaed) obervaon (graden) noe (graden)
7 Order k, dmenon m: Scang Propere j h ( j... h) j... h ( τ ) ( τ )...( τ n ) ( ν j... h = k m ξ + } x = A + n } Maxmum eparabe number of ource max : m 0 3 k Aume fu-rank A wh neary ndependen mxure combnaon Depend on he geomery of he ource drecon vecor reave o he array
8 Graden Fow Acouc Separaon Oudoor Envronmen 4 mcrophone whn 5 mm radu mae peaker a 0.5 m, awn urrounded by budng a 30 m cm
9 Graden Fow Acouc Separaon Indoor Envronmen 4 mcrophone whn 5 mm radu mae peaker a 0.5 m, reverberan room of dmenon 3, 4 and 8 m cm
10 Monaura Source Separaon: Pror Seecon Evdence of mxng mode : x( ( + n( Source eparaon from a nge ource ambguou, une he ource ( have a known rucure. The pror ha o be carefuy choen, accounng for he phyc of he probem.
11 Coherence a Acouc Pror Pror on ource mode : ~ ( ~ A ( ( θ ( ) ~ ( qua-perodc,.e. hor-erm perodc (evera cyce) Shor-erm coherence of a ource can be expreed n erm of me θ and ampude A fucuaon of a perodc waveform Thee fucuaon aow o dnguh and eparae he ource even f hey overap n he pecra doman.
12 Tme-Doman Monaura Separaon + x( ( n( ( A ( ( θ ( ) Succefu eparaon of wo frequency-chrped and ampudemoduaed quaperodc waveform. Separaon ucceed even hough harmonc of he nananeou frequence of he ource concde a wo nance of me. G.Cauwenbergh, Monaura Separaon of Independen Acouca Componen, ISCAS 99
13 Reaon o graden fow. A( ( θ ( ) A( ( ( + θ ( ( ) = A( ( + A( θ ( (. Ampude Co-Moduaon Phae Co-Moduaon Work n progre
14 Concuon A mehod for ocazng and eparang broadband wave propagang n free pace for array of dmenon maer han he hore waveengh n he ource ha been decrbed. Wave graden fow conver he probem o ha of ac ICA, wh mxng coeffcen yedng he drecon cone of he ource. The echnque baed on a merc of coherence ha expree each ource a a qua-perodc waveform wh random hor-erm me and ampude fucuaon wa preened. We pan o exend graden fow prncpe o monaura ource eparaon.
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