S 1 (f)S 2 (f)+θ 1 θ 2Sound sourcesS (f) LMicrophonesHead ofhumanoid robotFigure 1: 2 BSS2.1 K L L θ l (l =1, ··· ,L) (Figure 1)K = L ...X (f) =A(f)S (f) (1) X (f) =[X 1 (f) ,...,X K (f)] T S (f,t) =[S 1 (f) ,...,S L (f)] T A(f) =[A kl (f)] kl[·] ij i j · A(f)2.2 ICA BSS ICA (FDICA) (DFT) X(f,t) =[X 1 (f,t),...,X K (f,t)] T – W (f) =[W lk (f)] lk Y (f,t) =[Y 1 (f,t),...,Y K (f,t)] T Y (f,t) =W (f)X(f,t) (2) W (f) [ 〈W [i+1] (f) =η I − Φ (Y (f,t)) Y (f,t) H〉 ]W [i] (f)t+ W [i] (f) (3) I 〈·〉 tX H [i] i η Φ (Y (f,t)) [15]Φ (Y (f,t)) ≡[e j·arg(Y1(f,t)) ,...,e j·arg(YL(f,t))] T(4)arg(·) [8, 16] (a) Proposed two-stage BSSSourcesignalsS 1(f)A(f)S (f)2ObservedsignalsX (f) 1X (f)2SIMOmodelbasedICA(b) Simple combination of conventional ICA and binary maskSourcesignalsS (f)2ObservedsignalsS 1(f) X (f)A(f)ICAA 11(f)S 1(f,t)A 21(f)S 1(f,t)Binary maskprocessingY 1(f,t)A 12(f)S 2(f,t)Binary maskA (f)S (f,t) processing22 2Y 2(f,t)B 1(z)s 1(t)1 Y 1(f,t)X (f)2B (z)s (t)2 2Binary maskprocessingY 2(f,t)Figure 2: (a) 2 BSS(b) ICA (K = L =2)2.3 BSS [12, 13, 14] ICA BSS () –l l L =2l Ŷ l (f,t) =m l (f,t) X l (f,t) (5) m l (f,t) |X l (f,t)| >|X k (f,t)| (k ≠ l) m l (f,t) = 1m l (f,t) =0– ()3 2 BSS 3.1 SIMO-ICA [10,11] SIMO 24
SIMO-ICA SIMO Figure 2(a)SIMO-ICA 2 BSS SIMO-ICA ICA 2 (Figure 2(b)) [17] ICA Y l (f,t) =B l (f)S l (f,t) +E l (f,t) (l =1, ··· ,L)( B l (f) E l (f,t) ICA) E l (f,t) – 0 () Y 1 (f,t) Y 2 (f,t) ICA BSS SIMO-ICA SIMO-ICA SIMO A kl (f)S l (f,t) SIMO SIMO-ICA 3.2 SIMO-ICA [10] ICA SIMO SIMO-ICA SIMO-ICA (FD-SIMO-ICA) FD-SIMO-ICA (L − 1) FDICA fidelity controller(FC) ICA FD-SIMO-ICA l ICA (l =1,...,L− 1) []Y (ICAl) (f,t) = Y (ICAl)k(f,t) = W (ICAl) (f) X (f,t)k1(6)UnknownKnownS1(f) X1(f)A11(f)A12(f)A21(f)A22(f)S2(f) X2(f)FD-SIMO-ICAICA1-+-+++Fidelity controllerTo beindependent(ICA1)Y1(ICA1)Y2YY(ICA2)1(ICA2)2To beindependent(f,t)(f,t)(f,t)(f,t)Figure 3: K = L =2 FD-SIMO-ICA W (ICAl) (f) =[W (ICAl)ij (f)] ij l FDICAFC L−1∑Y (ICAL) (f,t) =X (f,t) − Y (ICAl) (f,t) (7)l=1Y (ICAL) (f,t) L ICA L ICA ICA Y (ICAL) (f,t) W (ICAl) (f) (l =1, ··· ,L− 1) (− ∑ L−1l=1 Y (ICAl)(f,t)) (7) ICA ∑ Ll=1 Y (ICAl)(f,t) SIMO [ ∑ Ll=1 A kl(f)S l (f,t)] k1 (= X(f,t)) (6) (7) SIMO Y (ICAl) (f,t) =diag [ A(f)PlT ]Pl S (f,t) (8) P l (l =1,...,L) ∑ Ll=1 P l =[1] ij [10] (8) l SIMO A kl (f)S l (f,t)SIMO-ICA L = K =2ICA [] TY (ICA1)1 (f,t), Y (ICA1)2 (f,t)=[A 11 (f)S 1 (f,t), A 22 (f)S 2 (f,t)] T , (9)[] TY (ICA2)1 (f,t), Y (ICA2)2 (f,t)=[A 12 (f)S 2 (f,t), A 21 (f)S 1 (f,t)] T , (10)P 1 = IP 2 =[1] ij − I 25
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