2-10-2
ଟνϟϯωϧ֊৐ӅΕϚϧίϑϞσϧͷ
εϖΫτϧแབྷࣄલֶशʹΑΔηϛϒϥΠϯυԻ‫ݯ‬෼཭ ∗˕ඉ‫( ࠸୎ޱ‬౦େӃ৘ใཧ޻)ɼُԬ߂࿨ (౦େӃ৘ใཧ޻ɼNTT)

1

͸͡Ίʹ

ۙࣅʹΑͬͯ࣌ؒप೾਺ྖҬͷ‫؍‬ଌ৴߸Λۙࣅ͢Δɽ

ϒϥΠϯυԻ‫ݯ‬෼཭ (Blind Source Separation; BSS) ͷ໰୊ͱ͸ɼԻ‫ݯ‬৴߸΍Ի‫͔ݯ‬ΒϚΠΫ·Ͱͷ఻ୡಛੑ͕ະ஌ͷ৔߹ʹɼෳ਺ͷԻ‫ݯ‬৴߸͕ࠞ߹͞Εͨ‫؍‬ଌ৴߸͔ΒԻ‫ݯ‬৴߸Λਪఆ͢Δ໰୊Ͱ͋ΔɽҰൠతʹ BSS ͷ໰୊Λෆྑઃఆ໰୊Ͱ͋Γɼղͨ͘Ίʹ͸ɼԻ‫ݯ‬৴߸ʹରͯ͠ͳΜΒ͔ͷԾఆΛཱͯղΛ‫ݶ‬ఆ͢Δඞཁ͕͋Δɽྫ͑͹ɼඇෛ஋ߦྻҼࢠ෼ղ(Non-negative Matrix Factorization; NMF)[1, 2] Ͱ͸ɼ‫؍‬ଌ৴߸ͷύϫʔεϖΫτϩάϥϜ͕‫ݶ‬ΒΕͨ਺ͷύϫʔεϖΫτϧʹΑͬͯߏ੒͞Ε͍ͯΔ͜ͱΛԾఆ͢Δ͜ͱͰɼ‫؍‬ଌ৴߸ͷύϫʔεϖΫτϩάϥϜ
Λ 2 ͭͷඇෛ஋ߦྻͷੵʹ෼ղ͢Δɽ·ͨචऀΒ͸ɼԻ‫ڹ‬Πϕϯτɼ࢒‫ڹ‬ɼԻ‫ݯ‬ͷ౸དྷํ޲ͳͲ͕ BSS ͷ໰୊Λղͨ͘Ίͷख͕͔Γͱ੒Γ͏Δ͜ͱʹண໨͠ɼଟνϟϯωϧ֊৐ӅΕϚϧίϑϞσϧͱ‫Ϳݺ‬ϞσϧΛ༻͍ͯɼԻ‫ڹ‬Πϕϯτɼ࢒‫ڹ‬ɼԻ‫ݯ‬ͷ౸དྷํ޲ਪఆ
ͳͲΛԻ‫ݯ‬෼཭ͱ౷߹తʹߦ͏ख๏ΛఏҊ͖ͯͨ͠[3, 4, 5]ɽ͜ͷख๏͸ɼԻ‫ݯ‬৴߸ͷύϫʔεϖΫτϧ
͕‫ݶ‬ΒΕͨ਺ͷύϫʔεϖΫτϧͷભҠʹΑͬͯද‫͖Ͱݱ‬ΔͱԾఆ͢Δ͜ͱͰɼBSS ͷ໰୊ʹ͓͍ͯղΛ‫ݶ‬ఆ͠ɼԻ‫ݯ‬෼཭ͷख͕͔Γ (ͷҰ෦) ͱ͢Δख๏
ͱͳ͍ͬͯͨɽ͔͠͠ɼNMF ΍ଟνϟϯωϧ֊৐ӅΕϚϧίϑϞσϧͳͲͷɼԻ‫ݯ‬৴߸ͷεϖΫτϧͷ
਺Λ੍‫͢ݶ‬ΔΞϓϩʔνͰ͸ɼԻ‫ݯ‬৴߸ΛΑΓৄࡉʹϞσϧԽ͠Α͏ͱͯ͠Ϟσϧʹ͓͚ΔύϫʔεϖΫτϧͷ਺Λ૿΍ͤ͹૿΍͢΄ͲɼBSS ͷ໰୊ʹཱ͓͍ͯͯΒΕ͍ͯͨԾఆΛऑΊɼղΛ‫ݶ‬ఆ͢Δ͜ͱ
͕Ͱ͖ͳ͘ͳΔͱ͍͏τϨʔυΦϑ͕ੜͯ͡͠·͏ɽͦ͜ͰຊߘͰ͸ɼ[6] ΍ [7] ͷख๏ͷΑ͏ʹɼιʔεϑΟϧλϞσϧʹ‫ͳͨ৽͍ͨͮج‬ԾఆΛಋೖ͢Δ͜
ͱΛߟ͑ΔɽιʔεϑΟϧλϞσϧͱ͸ɼԻ੠εϖΫτϧΛ੠ଳ‫ۦ‬ಈԻ‫( ݯ‬ιʔε) ͷεϖΫτϧͱ੠ಓ(ϑΟϧλ) εϖΫτϧͷੵͰදͤΔͱͨ͠ϞσϧͰ
͋Δɽ͜ͷԾఆ͕੒ΓཱͭͳΒ͹ɼԻ੠εϖΫτϧ
͸ɼෳ਺‫ݸ‬ͷιʔεεϖΫτϧͱෳ਺‫ݸ‬ͷϑΟϧλε
ϖΫτϧͷ૊Έ߹ΘͤͰͰද͢͜ͱ͕Ͱ͖Δɽ͜ΕʹΑΓɼQ(s) ‫ݸ‬ͷιʔεεϖΫτϧͱ Q(f ) ‫ݸ‬ͷϑΟϧλεϖΫτϧΛ༻͍Δ͜ͱͰɼQ(s) + Q(f ) ͷࣗ༝౓Ͱ Q(s) × Q(f ) ‫ݸ‬ͷεϖΫτϧΛද‫͢ݱ‬Δ͜ͱ͕Ͱ͖ΔɽຊߘͰ͸ɼιʔεϑΟϧλϞσϧʹ‫͍ͯͮج‬Ի‫ݯ‬৴߸ΛϞσϧԽ͠ɼϑΟϧλεϖΫτϧΛࣄલֶश
͢Δ͜ͱͰɼԻ‫ݯ‬৴߸ΛΑΓৄࡉʹϞσϧԽ͠ͳ͕Β΋ɼBSS ͷ໰୊ʹ͓͚ΔղΛे෼ʹ‫ݶ‬ఆ͠ɼԻ‫ݯ‬෼཭ੑೳΛ޲্ͤ͞Δख๏ΛఏҊ͢Δɽ

2ଟνϟϯωϧ֊৐ӅΕϚϧίϑϞσϧ

2.1 ৞ΈࠐΈࠞ߹ۙࣅʹΑΔ‫؍‬ଌ৴߸ͷࠞ߹ϞσϧI ‫ݸ‬ͷԻ‫͔ݯ‬Β౸དྷ͢Δ৴߸Λ M ‫ݸ‬ͷϚΠΫϩϑΥ
ϯͰ‫؍‬ଌ͢Δ৔߹Λߟ͑Δɽࣨ಺ΠϯύϧεԠ౴௕͕࣌ؒप೾਺ల։ͷ࣌ؒ૭௕ʹରͯ͠े෼ʹ୹͍ͱ‫ݶ‬Βͣɼॠ࣌ࠞ߹ۙࣅ͕੒Γཱͨͳ͍৔߹ (࢒‫͕͋ڹ‬Δ৔߹) Λߟ͑ɼ࣌ؒप೾਺ྖҬʹ͓͚Δ৞ΈࠐΈࠞ߹y(ωk , tl ) ≈

I 
T


ai (ωk , tτ )si (ωk , tl − tτ ).

(1)i=1 τ =0ͨͩ͠ɼ y(ωk , tl ) = (y1 (ωk , tl ), . . . , yM (ωk , tl ))T ∈CM ɼ ai (ωk , tτ ) = (ai,1 (ωk , tτ ), . . . , ai,M (ωk , tτ ))T ∈CM Ͱ͋Δɽ͜͜Ͱ ym (ωk , tl ) ∈ C ͸ m ൪໨ͷϚΠΫͰ‫؍‬ଌ͞Εͨ‫؍‬ଌ৴߸ͷप೾਺ ωk ɼ࣌ࠁ tl ʹ͓͚
Δ࣌ؒप೾਺੒෼Ͱ͋Γɼsi (ωk , tl ) ∈ C ͸ i ൪໨ͷԻ‫ݯ‬৴߸ͷप೾਺ ωk ɼ࣌ࠁ tl ʹ͓͚Δ࣌ؒप೾਺੒
෼Ͱ͋Δɽ·ͨ ai (ωk , tτ ) ͸ i ൪໨ͷԻ‫ݯ‬৴߸ʹର͢
Δप೾਺ ωk ʹ͓͚Δ఻ୡप೾਺ಛੑͷ࣌ࠁ tτ ͷ੒෼Ͱ͋Γɼ0 ≤ τ ≤ T ͸఻ୡप೾਺ಛੑͷ࣌ؒप೾਺ྖҬʹ͓͚Δ࣌ؒΠϯσοΫεͰ͋ΔɽҎԼͰ͸ωk ɼtl ΛͦΕͧΕ k ɼl ͷఴ͑ࣈͰද͢ɽ

2.2

ιʔεϑΟϧλϞσϧʹ‫ͮ͘ج‬Ի‫ݯ‬৴߸ͷੜ੒ϞσϧͰ͸ɼԻ‫ݯ‬৴߸ͷੜ੒ϓϩηεΛ֬཰తʹ‫ه‬ड़͢Δɽ·ͣԻ‫ݯ‬৴߸͕۠෼తʹఆৗͰ͋Δ͜ͱΛԾఆ
2͠ɼ֤࣌ؒप೾਺఺Ͱ si,k,l ͕ฏ‫ ۉ‬0ɼ෼ࢄ σi,k,lͷෳૉਖ਼‫ن‬෼෍ʹै͏ͱ͢ΔͱɼԻ‫ݯ‬৴߸ͷੜ੒ϓϩηε͸ɼ
2
si,k,l |σi,k,l ∼ NC (si,k,l ; 0, σi,k,l
)ɼ

(2)

2
ͱॻ͖දͤΔɽ͜͜Ͱ σi,k,l͸प೾਺ k ɼ࣌ࠁ l ʹ͓͚Δ i ൪໨ͷԻ‫ݯ‬ͷύϫʔεϖΫτϧີ౓Λද͢ɽ্‫ه‬ͷϞσϧʹ NMF ͷԾఆΛ૊ΈࠐΉͱɼ
2
σi,k,l= wi,k hi,l ,(3)ͱͳΔɽ্‫ه‬ͷࣜʹΑΔଟνϟϯωϧ‫؍‬ଌ৴߸ͷੜ੒Ϟσϧ͸ɼଟνϟϯωϧ NMF[8] ͱ‫ݺ‬͹Ε͍ͯΔɽ͜͜ͰɼιʔεϑΟϧλϞσϧʹ‫͖ͮج‬ɼi ൪໨ͷԻ‫ݯ‬ͷप೾਺ k ʹ͓͚Δ‫ج‬ఈύϫʔεϖΫτϧ͕ɼιʔ(s)(f )εεϖΫτϧ wi,k ͱɼϑΟϧλεϖΫτϧ wi,k ͷੵʹΑͬͯߏ੒͞ΕΔͱԾఆ͢Δͱɼ
(s)

(f )

wi,k = wi,k wi,k ,(4)ͱͳΔɽ͔͠͠ͳ͕ΒɼιʔεεϖΫτϧ΍ϑΟϧλ
εϖΫτϧ͸ɼൃ࿩಺༰ʹΑͬͯ࣌ؒมԽ͢Δͱߟ͑
ΒΕΔͷͰɼιʔεεϖΫτϧͷঢ়ଶΛද͢ӅΕม਺(s)zi,l ∈ 1, . . . , Q(s) ɼϑΟϧλεϖΫτϧͷঢ়ଶΛද͢(f )ӅΕม਺ zi,l ∈ 1, . . . , Q(f ) Λಋೖ͠ɼͦΕͧΕͷঢ়ଶͷ࣌‫͕ྻܥ‬Ϛϧίϑ࿈࠯ʹै͏ͱԾఆ͢Δɽ

zi,l |zi,l−1 ∼ Categorical(zi,l ; ρ

(s)

(s)

(s)

(s)

(f )

(f )

(f )

(f )

(s)

i,zi,l−1zi,l |zi,l−1 ∼ Categorical(zi,l ; ρ(f )i,zi,l−1

), ɹ

(5)

).

(6)
(s)

͜͜Ͱ Categorical(x; y) = yx Ͱ͋Γɼρi,q(s) =
(s)

(s)

(ρi,q(s) ,1 , . . . , ρi,q(s) ,Q(s) ) ͸ i ൪໨ͷԻ‫͚͓ʹݯ‬Διʔ
∗

Semi-blind source separation with multichannel factorial hidden Markov model using pretrained spectral envelope templates. by HIGUCHI, Takuya (The University of Tokyo), KAMEOKA Hirokazu (The
University of Tokyo, NTT)

日本音響学会講演論文集- 579 -

2015年3月

εͷঢ়ଶ q (s) ͔Β֤ঢ়ଶ 1, . . . , Q(s) ΁ͷભҠ֬཰Λ
(f )
(f )
(f )
ද͠ɼρi,q(f ) = (ρi,q(f ) ,1 , . . . , ρi,q(f ) ,Q(f ) ) ͸ i ൪໨ͷԻ‫͚͓ʹݯ‬ΔϑΟϧλͷঢ়ଶ q (f ) ͔Β֤ঢ়ଶ 1, . . . , Q(f )΁ͷભҠ֬཰Λද͢ɽঢ়ଶ q (s) Ͱ͋Δ i ൪໨ͷԻ‫ݯ‬ͷ(s)ιʔεεϖΫτϧΛ wi,k,q(s) ɼঢ়ଶ q (f ) Ͱ͋Δ i ൪໨ͦ͜Ͱ·ͣɼ[9] ͷख๏ͱಉ༷ʹɼθi ∈ {ϑ1 , . . . , ϑO }
Λ i ൪໨ͷԻ‫ݯ‬ͷ౸དྷํ޲ͱ͠ɼ֤Ի‫ݯ‬ͷ DOA ͕͜ͷ DOA ީิ஋ͷத͔Βܾఆ͞ΕΔͱԾఆ͢Δ͜ͱ
ͰɼԻ‫ ݯ‬i ͷ౸དྷํ޲ θi ͕ੜ੒͞ΕΔϓϩηεΛҎԼͷΑ͏ʹ‫ه‬ड़͢Δɻ
(o)

(s)

(f )

(s)

(f )

si,k,l |wi,k,1:Q(s) , wi,k,1:Q(f ) , hi,l , zi,l , zi,l∼ NC (si,k,l ; 0, w

(s)

(s)

i,k,zi,l

w

(f )

(f )

i,k,zi,l

hi,l ).
(7)

(j)

(j)

Λಋೖ͠ɼঢ়ଶͷ࣌‫ ྻܥ‬zi,1 , . . . , zi,L ͕Ϛϧίϑ࿈࠯ʹै͏ͱԾఆ͢Δɽ(j) (j)(j)(j)
zi,l |zi,l−1 ∼ Categorical(zi,l ; ρ (j)
i,z

).

(8)

i,l−1

(j)

͜ͷͱ͖ɼhi,l ͕Իྔͷঢ়ଶ zi,l ∈ 1, . . . , J ʹΑͬͯҟͳΔϋΠύʔύϥϝʔλΛ࣋ͭΨϯϚ෼෍ʹै͏ͱԾఆ͢Δͱɼ
(j)hi,l |zi,l ∼ Gamma(hi,l ; αz (j) βz(j) ),
i,l

i,l

(9)

ࠞ߹ DOA ϞσϧʹΑΔۭؒ૬ؔߦྻͷੜ੒Ϟσϧ࣍ʹۭؒ૬ؔߦྻͷੜ੒ϓϩηεΛ֬཰తʹϞσϧԽ͢Δɽ఺Ի‫ͱݯ‬ฏ໘೾౸དྷΛԾఆ͢Δͱɼۭؒ૬
ؔߦྻ͸Ի‫ݯ‬ͷ౸དྷํ޲ʹԠͯ͋͡Δಛఆͷߏ଄Λ࣋ͭɽྫ͑͹ɼϚΠΫϩϑΥϯͷ਺ M = 2 ͷ৔߹Ͱ͸ɼํ޲ θ(0 ≤ θ ≤ π) ʹ͋ΔԻ‫ݯ‬ͷۭؒ૬ؔߦྻ͸ɼҎԼͷΑ͏ʹཅʹ‫ه‬ड़Ͱ͖Δɽ



∗
1
J (θ, ω) = jωB cos θ/C 1 ejωB cos θ/C(10)e͜͜Ͱ j ͸‫਺ڏ‬୯ҐɼB [m] ͸ϚΠΫϩϑΥϯؒͷ‫ڑ‬཭ɼC [m/s] ͸Ի଎Ͱ͋Δɽi ൪໨ͷԻ‫ݯ‬ͷ౸དྷํ޲θi ͕‫ط‬஌ͷ৔߹Ͱ͸ɼ௚઀೾ʹରԠ͢Δۭؒ૬ؔߦ
ྻ͸ J (θi , ωk ) ͱ౳͘͠ͳΔ͜ͱ͕‫ظ‬଴͞ΕΔɽ͔͠͠ͳ͕Β࣮ࡍʹ͸ɼԻ‫ݯ‬ͷ౸དྷํ޲͸Ի‫ڹ‬৴߸͔Β௚઀‫؍‬ଌͰ͖ͳ͍͹͔ΓͰͳ͘ɼϑϨʔϜ಺ͷ࢒‫ڹ‬΍ϊΠζͳͲʹΑͬͯɼۭؒ૬ؔߦྻ͸ཧ૝తͳߏ଄͔
Βҳ୤͢Δ͜ͱ͕͋Δɽ

日本音響学会講演論文集

(11)
(12)

ׂ͕Γ౰ͯΒΕΔ͔Λද͢Πϯδέʔλม਺Ͱ͋Γɼ(o)(o)্ࣜ͸͜Ε͕཭ࢄ෼෍ (֤֬཰஋͕ ρ1 , . . . , ρO ) ͔Βੜ੒͞ΕΔ͜ͱΛҙຯ͍ͯ͠Δɻͦͯ͠ɼ௚઀೾ʹ(o)ରԠ͢Δۭؒ૬ؔߦྻ C i,k,0 ͕ɼzi ͕‫ط‬஌ͷ৚݅ԼͰɼҎԼͷΑ͏ͳ΢Οογϟʔτ෼෍ʹै͏ͱԾఆ͢Δɽ

C i,k,0 |zi∼ WC (C i,k,0 ; γ, J ϑ (o) ,k + I).
z

(13)

i

ͨ ͩ ͠
WC (X; γ, Y )∝|X|(γ−M )/2 exp(− 12 tr(XY −1 )) Ͱ ͋ Γɼγ ͸γ ≥ M + 1 Λຬͨ͢ϋΠύʔύϥϝʔλͰ͋Δɽ͜͜Ͱ͸ɼ‫ྻߦٯ‬ԋࢉΛՄೳʹ͢ΔͨΊʹɼۙࣅతʹ J ϑ (o) ,k ʹඍখ஋ Λ༻͍ͯ୯Ґߦྻ I Λ଍
z

i

(o)

ͯ͋͠Δɽ͜͜ͰӅΕม਺ zi Λਪఆ͢Δ͜ͱ͕ɼԻ‫ݯ‬ͷ౸དྷํ޲ਪఆΛߦ͏͜ͱʹ૬౰͍ͯ͠Δɽ‫ ؍‬ଌ ৴ ߸ ͷ ࠷ ऴ త ͳ ੜ ੒ Ϟ σ ϧ ͸ a1:I,k,0:T ɼ
(s)
(f )
(s)
w1:I,k,1:Q(s) ɼw1:I,k,1:Q(f ) ɼh1:I,l−T :l ɼz1:I,l−T :l ɼ(f )z1:I,l−T :l ͕‫ط‬஌ͷ৚݅ԼͰɼࣜ (5)ɼࣜ (6)ɼࣜ (8)ɼ
ࣜ (9)ɼࣜ (13) ͱ߹ΘͤͯҎԼͷΑ͏ʹॻ͖௚ͤΔɽ
(s)

(f )

y k,l |a1:I,k,0:T , w1:I,k,1:Q(s) , w1:I,k,1:Q(f ) ,
(s)

(f )

h1:I,l−T :l , z1:I,l−T :l , z1:I,l−T :l

(s)
(f )
∼ NC (y k,l ; 0,C i,k,τ w(s) w(f ) hi,l−τ ).
i,τ(j)ؔ਺Ͱ͋Δɽzi,l ͕ແԻঢ়ଶʹରԠ͢Δͱ͖͸ hi,l ͸

2.3

(o)

i

ͱͳΔɽ͜͜Ͱ α1:J ͱ β1:J ͸ͦΕͧΕΨϯϚ෼෍ͷ‫ܗ‬ঢ়ύϥϝʔλͱεέʔϧύϥϝʔλͰ͋Γɼ
α−1 −x/βe
Gamma(x; α, β) = x Γ(α)βɼͨͩ͠ Γ(·) ͸ΨϯϚαখ͞ͳ஋Λͱͬͯ΄͍͠ͷͰɼখ͞ͳ஋ΛͱΔ֬཰͕
ߴ͘ͳΔΑ͏ʹΨϯϚ෼෍ͷϋΠύʔύϥϝʔλΛ(j)ઃఆ͠ɼzi,l ͕༗Իঢ়ଶʹରԠ͢Δͱ͖͸Ұ༷෼෍ʹ
ۙ͘ͳΔΑ͏ʹΨϯϚ෼෍ͷϋΠύʔύϥϝʔλΛઃఆ͢Ε͹Α͍ɽ(o)(o)
zi ∈ {1, . . . , O} ͸ i ൪໨ͷԻ‫Ͳʹݯ‬ͷ DOA ީิ஋(o)࣍ʹɼԻ‫ݯ‬ͷԻྔʹண໨͢ΔͱɼແԻঢ়ଶͱ༗Ի
ঢ়ଶͰ͸౰વԻྔͷେ͖ͳ஋ͷऔΓ΍͕͢͞ҟͳΔ
ͱߟ͑ΒΕΔͷͰɼԻྔ΋·ͨԻ‫ݯ‬ͷঢ়ଶ (Ի‫ڹ‬Πϕϯτ) ʹґଘͯ͠ҟͳΔৼΔ෣͍Λ͢Δͱ͍͑Δɽͦ(j)͜Ͱɼ·ͣԻྔͷঢ়ଶΛද͢ӅΕม਺ zi,l ∈ 1, . . . , J(o)zi |ρi ∼ Categorical(zi ; ρi ),θi = ϑz(o) .

(f )ͷԻ‫ݯ‬ͷϑΟϧλεϖΫτϧΛ wi,k,q(f ) ͱද͢ͱ͢
Δͱɼ࣌ࠁ l ʹ͓͚Δ i ൪໨ͷԻ‫ݯ‬৴߸ͷιʔεεϖ(s)(f )ΫτϧͱϑΟϧλεϖΫτϧ͸ zi,l ͱ zi,l ʹͦΕͧΕґଘ͠ɼsi,k,l ͷੜ੒Ϟσϧ͸ҎԼͷΑ͏ʹॻ͖௚ͤΔɽ

i,k,zi,l

i,k,zi,l(14)͜ͷੜ੒Ϟσϧʹ‫࠷͍ͯͮج‬దͳύϥϝʔλΛ‫ٻ‬ΊΔ͜ͱ͸ɼιʔεϑΟϧλϞσϧʹΑͬͯԻ‫ݯ‬৴߸ͷࣗ༝౓Λ‫ݶ‬ఆ͠ͳ͕ΒɼԻ‫ݯ‬ͷ౸དྷํ޲ਪఆɾ࢒‫ڹ‬আ‫ڈ‬ɾԻ‫ڹ‬Πϕϯτ‫ݕ‬ग़ɾԻ‫ݯ‬෼཭ͷ໰୊Λ౷߹తʹղ͘͜ͱʹ૬౰͍ͯ͠Δɽ

3

ิॿؔ਺๏ʹ‫ͮ͘ج‬ύϥϝʔλਪ࿦ΞϧΰϦζϜ໨తؔ਺Ͱ͋Δର਺ࣄ‫Ͱ཰֬ޙ‬͸֤ύϥϝʔλ͕ෳࡶʹؔ܎͠߹͓ͬͯΓɼҰൠతʹ࠷దԽ͕ࠔ೉Ͱ
͋Δɽͦ͜Ͱޮ཰తʹ࠷దͳύϥϝʔλΛ‫ٻ‬ΊΔ൓෮ΞϧΰϦζϜΛɼิॿؔ਺๏ͷ‫ݪ‬ཧʹ‫͖ͮج‬ಋग़
͢ΔɽϞσϧʹ͓͚Δਪఆ͍ͨ͠ม਺͸ W (s) =(s)(f )w1:I,1:K,1:Q(s) , W (f ) = w1:I,1:K,1:Q(f ) , H = h1:I,1:L ,C = C 1:I,1:K,0:T Ͱ͋Δɽ্‫ه‬ͷม਺ͷू߹Λ Θ Ͱ
(j)
(o)
(s)
ද͢ɽZ (j) = z1:I,1:L ɼZ (o) = z1:I ɼZ (s) = z1:I,1:L ɼ(f )Z (f ) = z1:I,1:L ͸ӅΕม਺ͱ͢ΔɽҎԼͰ͸ ρ(s) ɼρ(f ) ɼρ(j) ɼρ(o) ͸࣮‫ݧ‬తʹఆΊΒΕͨఆ਺ͱ͢Δɽ
ิॿม਺ͷू߹Λ Λ ͱ͢Δͱɼ໨తؔ਺ L(Θ) =log p(Θ|Y ) ʹର͢Δิॿؔ਺ L+ (Θ, Λ) ͸ҎԼͷΑ͏ʹઃ‫͖Ͱܭ‬Δɽ
L+ (Θ, Λ)- 580 -

2015年3月

=−

1
2
k,l




i,q (s) ,q (f ) ,τ

 
(s)
(f )
λq(s) ,i,l−τ λq(f ) ,i,l−τ tr y k,l y k,l H

Ri,k,l,τ,q(s) ,q(f ) C −1
i,k,τ
(s)

(f )

Ri,k,l,τ,q(s) ,q(f ) /wi,k,q(s) wi,k,q(f ) hi,l−τ

(s)
(f )
+ tr U −1
k,l C i,k,τ wi,k,q (s) wi,k,q (f ) hi,l−τ (j) λj,i,l (αj − 1) log hi,l − hi,l /βj++ log |U k,l |j,i,l− αj log βj − log Γ(αj )Fig. 1 ΫϦʔϯͳԻ੠͔Β STRAIGHT[12] ʹΑͬͯநग़࣮͠‫͍ͨ༻ʹݧ‬ϑΟϧλεϖΫτϧͷྫɽ1 −1di,o − tr C i,k,0 (J k,o + I)
+
2
i,k,o
 

(s)
(f )
Ri,k,l+τ,τ,q(s) ,q(f ) /wi,k,q(s) wi,k,q(f ) hi,l−1
γ−M
tr Ũ i,k C i,k,0 + log |Ũ i,k |
+


2
(s)
(f )
−1
 (s)
 (f )+ tr U k,l+τ C i,k,τ wi,k,q(s) wi,k,q(f ) hi,l ,
λq(s) ,i,l log p(Z (s) ) +λq(f ) ,i,l log p(Z (f ) )+(21)
q (s) ,i,lq (f ) ,i,l
 (j)λj,i,l log p(Z (j) ) + CL+ ,
(15)
+
(f )
Ͱ͋Δɽ͞Βʹ λq(f ) ,i,l ͷ౳߸੒ཱ৚݅ʹؔͯ͠΋
j,i,lForward-Backward ΞϧΰϦζϜΛ༻͍ͯɼ (f )͜ ͜ Ͱ
Ri,k,l,τ,q(s) ,q(f ) ɼU k,l ɼŨ i,k
͸
(f )
(f )
(f )
(f )
λ
=
F
B
/
Fq(f ) ,i,l Bq(f ) ,i,l , (22)
(f
)
(f
)
(f
)
q ,i,lq ,i,l q ,i,lR=
IΛຬͨ͢Τϧϛʔτਖ਼(s) ,q (f )i,k,l,τ,q
i,τ
(s)

(f )

(s)
q (s) λq (s) ,i,l = 1ɼq (f )(j)ఆ ஋ ߦ ྻ Ͱ ͋ Γɼλq(s) ,i,l ɼλq(f ) ,i,l ɼλj,i,l ɼdi,o ͸(f )q (f ) λq (f ) ,i,l = 1ɼ(j)j λj,i,l = 1ɼ

(f )

(f )

Fq(f ) ,i,l = p(Θ|zi,l = q (f ) )o di,o = 1 ΛͦΕͧΕຬͨ͢ඇෛ஋ͷεΧϥʔ஋Ͱ

͋ΔɽCL+ ͸ఆ਺߲Λ·ͱΊͨ΋ͷͰ͋Δɽࣜ (15)ͷ౳߸੒ཱ৚݅͸ɼRi,k,l,τ,q(s) ,q(f ) ͱ U k,l ʹؔ͠
ͯ͸
(s)

(f )
Bq(f ) ,i,l =U k,l = X̂ k,l ,(f )p(Θ|zi,l = q (f ) ) 
1  (s)∝ exp −
λq(s) ,i,l tr y k,l+τ y k,l+τ H
2
(s)

(17)

k,τ,q

i,k,zi,l−τ

Ri,k,l+τ,τ,q(s) ,q(f ) C −1
i,k,τ
(s)



q (s)

(s)(f )Ri,k,l+τ,τ,q(s) ,q(f ) /wi,k,q(s) wi,k,q(f ) hi,l


(s)
(f )
+ tr U −1
Cw
hw,
k,l+τ i,k,τ
i,k,q (s) i,k,q (f ) i,l

q (s)

(s)

(23)

(f )
(f )
(f )
Bq(f ) ,i,l+1 p(Θ|zi,l+1 = q (f ) )ρi,q(f ) ,q(f ) ,ͨͩ͠ͷ౳߸੒ཱ৚݅ʹؔͯ͠͸ Forward-Backward ΞϧΰϦζϜΛ༻͍ͯɼ
 (s)
(s)
(s)
(s)
(s)
λq(s) ,i,l = Fq(s) ,i,l Bq(s) ,i,l /Fq(s) ,i,l Bq(s) ,i,l , (18)
(s)

(f )

(24)

Ͱ ͋ Δ ɽͨ ͩ ͠=X̂ k,l
(s)
(f )
(s)
w
hi,l−τ Ͱ͋Δɽλq(s) ,i,l(s)
(f )i,τ C i,k,τ w

Fq(s) ,i,l = p(Θ|zi,l = q (s) )q (f )

q (f )

(f )Fq(f ) ,i,l−1 ρi,q(f ) ,q(f ) ,

−1

(f )

Ri,k,l,τ,q(s) ,q(f ) = C i,k,τ wi,k,q(s) wi,k,q(f ) hi,l−τ X̂ k,l ,(16)

i,k,zi,l−τ





(s)

(25)

Fq(s) ,i,l−1 ρi,q(s) ,q(s) ,(j)Ͱ͋ΔɽŨ i,k ɼdi,o ɼλj,i,l ͷ౳߸੒ཱ৚݅͸ɼ[5] ͱಉ༷Ͱ͋Δɽࢴ໘ͷ౎߹্ৄࡉ͸লུ͢Δ͕ɼͦͷଞ

(s)
(s)
(s)
(s)
Bq(s) ,i,l+1 p(Θ|zi,l+1 = q (s) )ρi,q(s) ,q(s) , ͷύϥϝʔλͷߋ৽ଇ͸ L+ ͷภඍ෼Λ 0 ͱஔ͘͜Bq(s) ,i,l =ͱͰಋ͚Δɽ
q (s)
(20)

(19)

4

ͨͩ͠
(s)
p(Θ|zi,l = q (s) ) 
1  (f )∝ exp −λq(f ) ,i,l tr y k,l+τ y k,l+τ H
2
(f )
k,τ,q

Ri,k,l+τ,τ,q(s) ,q(f ) C −1
i,k,τ

日本音響学会講演論文集ධՁ࣮‫ݧ‬

4.1 Ի‫ݯ‬෼཭ੑೳͷධՁ࣮‫ݧ‬ఏҊ๏ͷԻ‫ݯ‬෼཭ੑೳͷධՁͷͨΊʹɼ࢒‫ڹ‬ԼͰͷ൒‫͋ࢣڭ‬ΓԻ‫ݯ‬෼཭࣮‫ݧ‬ΛߦͬͨɽATR Ի੠σʔλϕʔε [10] ͷதͷ 3 ਓͷൃ࿩ऀ (ঁੑ 2 ਓɼஉੑ 1 ਓ)ʹΑΔ 15 छྨͷൃ࿩ʹରͯ͠ɼRWCP σʔλϕʔε[11] ͷΠϯύϧεԠ౴ (࢒‫ ؒ࣌ڹ‬380 msɼϚΠΫؒ‫ڑ‬
཭ 11.48 cmɼϚΠΫͷ਺ M = 2) Λ৞ΈࠐΈɼਓ޻

- 581 -

2015年3月

10(a)

SIR Improvement [dB]SDR Improvement [dB]

3.5
3
2.5
2
1.5
1
0.5
0

(b)

9.5
9
8.5

ᥦ᱌ἲ 䠄ܳሺ௦ሻ ൌ ͸䠅8ᥦ᱌ἲ 䠄ܳሺ௦ሻ ൌ ͳͷ䠅ᥦ᱌ἲ 䠄ܳሺ௦ሻ ൌ ͵Ͳ䠅

7.5

ᚑ᮶ἲ
7

15

30

45

ᥦ᱌ἲ䛻䛚䛡䜛䝣䜱䝹䝍䝇䝨䜽䝖䝹ᚑ᮶ἲ䛻䛚䛡䜛䝟䝽䞊䝇䝨䜽䝖䝹

60

䛾ᩘ

15

30

45

ᥦ᱌ἲ䛻䛚䛡䜛䝣䜱䝹䝍䝇䝨䜽䝖䝹ᚑ᮶ἲ䛻䛚䛡䜛䝟䝽䞊䝇䝨䜽䝖䝹60

䛾ᩘ

Fig. 2 ఏҊ๏ʹ͓͚ΔϑΟϧλεϖΫτϧͷ਺΍ैདྷ๏ [5] ʹ͓͚Δ‫ج‬ఈύϫʔεϖΫτϧͷ਺Λม࣮͑ͯ‫ݧ‬Λߦͬͨͱ͖ʹಘΒΕͨ෼཭Իͷ (a)SDR ͷվળྔͱ (b)SIR ͷվળྔɽతʹଟνϟϯωϧͷࠞ߹৴߸Λ 5 ͭ࡞੒ͨ͠ɽ3 ͭͷԻ‫ݯ‬͸ΠϯύϧεԠ౴Λ৞Έࠐ·ΕΔ͜ͱͰϚΠΫ͔
Β 30◦ ɼ90◦ ɼ130◦ ͷҐஔʹਓ޻తʹͦΕͧΕ഑ஔ͞ΕͨɽαϯϓϦϯάप೾਺͸ 16 kHz ͱͨ͠ɽϑϨʔϜ௕ 64 msɼϑϨʔϜγϑτ௕ 16 ms Ͱ STFT Λߦ͍ɼ࣌ؒप೾਺ల։Λߦͬͨɽ΢Οογϟʔτ෼෍ͷϋΠύʔύϥϝʔλ γ ͸ 3 ͱͨ͠ɽιʔεεϖΫτϧ
ͷঢ়ଶ਺ Q(s) Λ 6ɼ15ɼ30ɼϑΟϧλεϖΫτϧͷ
ঢ়ଶ਺ Q(f ) Λ 15ɼ30ɼ45ɼ60 ͱͦΕͧΕม࣮͑ͯ‫ݧ‬ͨ͠ɽ = 10−3 ɼ౸དྷํ޲ͷ෼ׂ਺ O = 30 ͱͨ͠ɽԻྔͷঢ়ଶ਺ J = 2 ͱ͠ɼα1 ͱ β1 Λ 1ɼ10−3 ͱͦΕͧΕઃఆ͠ɼα2 ͱ β2 Λ 1 ͱ 1010 ͱઃఆ͢Δ͜ͱͰɼ
j = 1 ΛແԻঢ়ଶͱΈͳͨ͠ɽρ(j) ͸ i = 1, . . . , 3 ʹ(j)(j)͓͍ͯ ρi,1 = (0.9, 0.1)ɼρi,2 = (0.1, 0.9) ͱ͠ɼࣗ‫ݾ‬ͱͨ͠ɽC ͷભҠͷ֬཰ΛߴΊʹઃఆͨ͠ɽT = 3 √ॳ‫ظ‬஋͸ɼτ = 0 ͷ੒෼ʹؔͯ͠͸ 1/ M × I ͱ͠ɼτ = 1 : T Ͱ͸ 10−2 ×I ͱͨ͠ɽH ͷॳ‫ظ‬஋͸͢΂ͯͷཁૉΛ 1 ͱͯ͠༩͑ͨɽλ(q) ͷॳ‫ظ‬஋͸ 1/Qɼλ(j)ͷॳ‫ظ‬஋͸ 1/J ͱͨ͠ɽW (f ) ͸ɼSTRAIGHT[12]Λ༻͍ͯࠞ߹Ի੠ͱ͸ผͷൃ࿩͔Βநग़ͨ͠εϖΫτϧแབྷʹରͯ͠ HMM ֶश͢Δ͜ͱͰ 3 ਓͷ࿩ऀͷൃ࿩͔Β Q(f ) /3 ֶͭͣͭश͠ɼ‫ݻ‬ఆͨ͠ɽFig. 1
ʹֶशͨ͠ϑΟϧλεϖΫτϧͷҰྫΛࣔ͢ɽW (s)͸ɼSTRAIGHT Λ༻͍ͯநग़ͨ͠εϖΫτϧแབྷ‫ܥ‬ྻͰεϖΫτϩάϥϜΛׂͬͨ΋ͷΛιʔε੒෼ͱ‫ݟ‬ͳ͠ HMM ֶशΛͨ͠΋ͷΛॳ‫ظ‬஋ͱ͠ɼ൓෮ΞϧΰϦζϜʹΑΓߋ৽ͨ͠ɽρ(s) ɼρ(f ) ͸Ұ༷ͱͨ͠ɽd ͷॳ‫ظ‬஋͸౸དྷํ޲Λࡾ౳෼͢ΔΑ͏ʹઃఆͨ͠ɽ
·ͨɼθi ͷऔΓ͏ΔൣғΛ ϑ1+10(i−1) ͔Β ϑ10i ʹ‫ݶ‬ఆ͠ɼ֤Ի‫ʹͱ͝ݯ‬ਪఆ͢Δ౸དྷํ޲͕ॏͳΒͳ͍Α͏ʹ ρ(o) Λઃఆͨ͠ɽύϥϝʔλਪ࿦ΞϧΰϦζ
Ϝ͸ 50 ճ൓෮ͨ͠ɽલষͱಉ༷ʹ๬·͘͠ͳ͍‫ॴہ‬ղΛආ͚ΔͨΊɼ࠷ॳͷ 25 ճͷ൓෮͸ T = 0 ͱ͠ɼͦͷ‫ޙ‬ঃʑʹ T Λ 3 ͱͳΔ·Ͱ૿΍͠ͳ͕Β൓෮͠
ͨɽ·ͨɼ࠷ॳͷ 25 ճͷ൓෮͸ W Λߋ৽͠ɼͦͷ‫ ޙ‬T Λ૿΍͠ T > 0 ͱͳ͔ͬͯΒ͸ W Λߋ৽ͤͣʹ‫ݻ‬ఆͨ͠ɽൺֱର৅ʹ͸ [5] ͷख๏Λ༻͍ͨɽൺֱ
ख๏Ͱ͸ɼ෼཭ʹ༻͍Δࠞ߹Իͱ͸ผͷൃ࿩͔Βֶशͨ͠‫ج‬ఈύϫʔεϖΫτϧΛ W ͷॳ‫ظ‬஋ͱͯ͠༻͍
ͨɽ·ͨ‫ج‬ఈύϫʔεϖΫτϧͷঢ়ଶ਺ Q Λ 15ɼ30ɼ
45ɼ60 ͱͦΕͧΕม࣮͑ͯ‫ͨ͠ݧ‬ɽ෼཭Ի͸ଟνϟϯωϧ΢ΟʔφʔϑΟϧλʹΑͬͯಘͨɽԻ‫ݯ‬෼཭ɼ࢒‫ڹ‬আ‫ڈ‬ͷ٬‫؍‬ධՁ‫ج‬४ͱͯ͠ɼ࢒‫ڹ‬আ‫ࡁڈ‬Έ෼཭Իͷৼ෯εϖΫτϩάϥϜʹରͯ͠ɼࣨ಺ΠϯύϧεԠ౴Λ৞ΈࠐΉલͷԻ‫ݯ‬৴߸ͷৼ෯εϖΫτϩάϥϜΛࢀর͢Δ͜ͱͰಘΒΕͨ SDRɼSIR[13] Λ༻͍ͨɽ෼཭ॲཧલͷ SDRɼSIR ͸ͦΕͧΕ-4.77, -0.96[dB]Ͱ͋ͬͨɽFig. 2 ʹɼຊ࣮‫ʹݧ‬ΑͬͯಘΒΕͨ෼཭Իͷ SDRɼSIR ͷվળྔΛͦΕͧΕࣔ͢ɽఏҊ๏ʹ͓͚ΔιʔεεϖΫτϧ΍ϑΟϧλεϖΫτϧͷ਺ɼैདྷ๏ʹ͓͚

日本音響学会講演論文集Δ‫ج‬ఈύϫʔεϖΫτϧͷ਺ʹΑͬͯมಈͯ͠͸͍
Δ͕ɼఏҊ๏ʹΑͬͯಘΒΕͨ෼཭Իͷ٬‫؍‬ධՁ஋͸ɼैདྷ๏ʹΑͬͯಘΒΕͨ෼཭Իͷ٬‫؍‬ධՁ஋Λ্
ճΔ܏޲͕‫ݟ‬ΒΕͨɽಛʹ Q(s) = 6, 15 ͷͱ͖ͷఏҊ๏Λ༻͍ͯಘΒΕͨ෼཭Ի͸ɼैདྷ๏ʹΑͬͯಘΒΕͨ෼཭ԻΑΓ૯ͯ͡ߴ͍ SDR ͱ SIR Λࣔͨ͠ɽ
SDR ͸ Q(s) = 15ɼQ(f ) = 45 ͷͱ͖࠷΋ߴ͍஋Λࣔͨ͠ɽ͜ΕʹΑΓɼԻ‫ݯ‬෼཭ʹ͓͚ΔఏҊ๏ͷ༗ޮੑ͕ࣔ͞Εͨɽ

5͓ΘΓʹຊߘͰ͸ɼιʔεϑΟϧλϞσϧʹ‫͍ͯͮج‬Ի‫ݯ‬৴߸ΛϞσϧԽ͠ɼଟνϟϯωϧ֊৐ӅΕϚϧίϑϞσ
ϧʹ૊ΈࠐΉ͜ͱʹΑͬͯɼैདྷ๏Λ্ճΔੑೳΛ࣮‫͢ݱ‬ΔԻ‫ݯ‬෼཭ख๏ΛఏҊͨ͠ɽँࣙ ຊ‫ڀݚ‬͸ JSPS Պ‫ݚ‬අ 26730100 ͷॿ੒Λड͚ͨ΋ͷͰ͢ɽ

ࢀߟจ‫ݙ‬[1] D. D. Lee, and H. S. Seung, Nature, vol. 401,
pp.788–791, 1999.
[2] P. Smaragdis, and J. C. Brown, WASPAA 2003,
pp. 177–180, Oct. 2003.
[3] T. Higuchi, et al., Interspeech 2014, pp. 850–854,
2014.
[4] T. Higuchi and H. Kameoka, “Joint audio source
separation and dereverberation based on multichannel factorial hidden Markov model,”MLSP 2014.
[5] ඉ‫ ޱ‬ଞ, “ଟνϟϯωϧ֊৐ӅΕϚϧίϑϞσϧͱࠞ߹ DOA ϞσϧʹΑΔԻ‫ݯ‬෼཭ɾ౸དྷํ޲ਪఆɾ
Ի‫ڹ‬Πϕϯτ‫ݕ‬ग़ɾ࢒‫ڹ‬আ‫ڈ‬ͷ౷߹తΞϓϩʔν,”ిࢠ৘ใ௨৴ֶձٕज़‫ڀݚ‬ใࠂ, ి‫ؾ‬Ի‫ڹ‬ɼ2015[to appear].
[6] H. Kameoka and K. Kashino, ISCAS2009, pp.
2477–2480, May 2009.
[7] ٢Ҫ࿨Ղ, ‫ޙ‬౻ਅ޹, ৘ใॲཧֶձ‫ڀݚ‬ใࠂ, 2012–
MUS–96–8, Aug. 2012.
[8] H. Sawada et al., ICASSP 2012, pp. 261–264,
2012.
[9] ُԬ ଞ, Իߨ࿦ (य़), 1–1–19, pp.713-716, Mar.
2012.
[10] A. Kurematsu et al., Speech Communication,
pp. 357–363, 1990.
[11] S. Nakamura et al., LREC 2000, pp. 965–968,
2000.
[12] H. Kawahara et al, Speech Communication, vol.
27, no. 3–4, pp. 187–207, 1999.
[13] E. Vincent et al., IEEE Transactions on Audio, Speech, and Language Processing, pp. 1462–
1469, 2006.

- 582 -

2015年3月