調波パラメトリックNMFによる楽器演奏音響信号の分析合成

NMF 1. Nonnegative Matrix Factorization(HPNMF) MIDI 2 () [1] () HPNMF HPNMF (F0) HPNMF2. 1) (F0) 2) HPNMF NMF [2] Analysis and Synthesis of Instrument Performance Audio Signal UsingHarmonic-Domain Parametric NMF: Naoki Yasuraoka, KatsutoshiItoyama, Toru Takahashi, Tetsuya Ogata, and Hiroshi G. Okuno (KyotoUniv.) 1: NMF NMF i Y t, f ,i K W f ,k U i,k,t (t f )Y t, f ,i =K∑k=1W j,k U i,k,t(W j,k ,U i,k,t > 0 ) (1) U i,k,t X t, f ∑ t, f D ( X t, f∣ ∣∣ ∣∑i Y t, f ,i) W f ,k 1) 2) NMF3. NMF NMF NMF(HPNMF) NMF J φ t,ij, f NMF Y t, f ,i = ∑φ t,ij, fj( K∑k=1W j,k U i,k,t)j NMF NMF 1 2 [1, 3] (− (ω f − jµ t,i ) 2φ t,ij, f = ⎧⎨⎩exp(exp − (ω f −υ j ) 22σ 2 )2γ 2 )( j = 1,...,H)( j = H + 1,...,J)ω f f (Hz) σ 2 ,γ 2 {υ j } H+1≤ j≤J σ 2 γ 2 υ j {φ t,ij, f } 1≤ j≤H F0 µ t,i F0(2)(3)

1: 1. 0 1 :- (), -, -,-2 , -,-, -, -, -2 2. 0 1 3. 1 2 2 U i,k,t ∗ NMF HPNMF HPNMF {µ t,i ,W j,k ,U i,k,t } U i,k,t 4. HPNMF 4.1 [4] Standard MIDI File 1 NMF U i,k,t W j,k F0 µ t,i 1) F0 2) 2 4.2 Y t, f = ∑ i Y t, f ,i X t, f D I [5] minimize ∑t, f(X t, f log X t, fY t, f− ( X t, f −Y t, f) ) (4) µ t,i W j,k [2, 3] 1 Y t, f Jensen log 1 ≤Y t, f∑j,i,kλ t, fi, j,k(logλ t, fi, j,kφ t,ij, f W j,kU i,k,t) λ t, ft, fi, j,k ∀t, f ,i, j,k : λi, j,k > 0,∀t, f : ∑ i, j,k λ t, fi, j,k = 1 (4) 1 log(1/Y t, f )∑t, f ,i, j,k(λ t, fi, j,k X t, f logλ t, fi, j,kφ t,ij, f W + φ t,i(6)j,kU i,k,t ( µ t,i ,W j,k ) (6) j, f W j,kU i,k,t)∗ {φ t,ij, f } H+1≤ j≤J t,i (5) 2: SNR HPNMF NMFViolin 2.79 dB 2.40 dBCello 2.77 dB 2.51 dBFlute 2.02 dB 1.28 dB 2: ()() HPNMF () NMF 4.3kHz3.22.11.10.00.04.3kHz0.5 1.0 1.5 2.0sec.3.22.11.10.00.04.3kHz0.5 1.0 1.5 2.0sec.3.22.11.10.00.0 0.5 1.0 1.5 2.0sec. (4) (6) λ t, fi, j,k ← W j,kU i,k,t φ t,ij, f(7)Y t, fW j,k ← ∑ t, f ,i λ t, fi, j,k X t, f∑ t, f ,i U i,k,t φ t,ij, f, µ t,i ← ∑H j=1 j ∑ f ,k ω f λ t, fi, j,k X t, f∑ H j=1 j2 ∑ f ,k λ t, fi, j,k X (8)t, f (6) 2 µ t,i [3]5. HPNMF CD :Violin, Flute, Cello 3 9 , 4/5 , 1/5 . NMF HPNMF (SNR) . 2 SNR 2SNR HPNMF NMF HPNMF NMF [1]6. HPNMF (S), COE, CrestMuse .[1] : . , 2010-MUS-86, 2010.[2] Lee et al.: Algorithms for Non-negative Matrix Factorization. InProc. NIPS, pp. 556–562, 2000.[3] Kameoka et al.: Speech Spectrum Modeling for Joint Estimation ofSpectral Envelope and Fundamental Frequency. IEEE Trans. Audio,Speech and Lang. Process., Vol. 18, No. 6, pp. 1507–1516, 2010.[4] Teramura et al.: Gaussian Process Regression for Rendering MusicPerformance. In Proc. ICMPC, pp. 167–172, 2008.[5] FitzGerald et al.: On the Use of the Beta Divergence for MusicalSource Separation. In Proc. ISSC, pp. 1–6, 2009.