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独立低ランク行列分析を用いた
インラタクティブ音源分離
AS2 06番
北村研究室
大島風雅
はじめに
• 音源分離とは複数の音響信号
が
混
ざ
った観測信号から混合
前の信号を推定する技術
• 応用例
- 音声認識の前段処理
- 混合音楽信号の各パートに分離
2
∼∼∼∼
はじめに
• ブラインド音源分離(BSS)は混合系が不明な観測信号か
ら混合前の音源を推定する技術
• 独立成分分析(ICA)に基づく手法が発展してきた
• 音源間の統計的独立性を最大化する音源分離手法
3
音源 観測信号 推定信号
Ai
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Wi
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独立成分分析(ICA)
[Comon, 1994]
周波数領域ICA(FDICA)
[Smaragdis, 1998]
独立ベクトル分析(IVA)
[Kim et al., 2006]
独立低ランク行列分析(ILRMA)
[Kitamura et al., 2016]
多チャネル信号の
ブラインド音源分離手法
はじめに
• 最新手法である独立低ランク行列分析(ILRMA)は音源
間の独立性に加えて,低ランク音源モデルを導入した反復
最適化アルゴリズム
4
✓
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f(✓)
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✓0
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✓0
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局所最適解
最適解
ユーザの介入
変数
目的関数
定式化
• 時間的に変化するスペクトルの表現
- 短時間フーリエ変換(short-time Fourier transform: STFT)
5
時間波形
…
スペクトログラム
複素数要素を持つ行列
周波数
時間
…
時間領域 時間周波数領域
窓関数
シフト長
フーリエ変換長
離散フーリエ変換
離散フーリエ変換
離散フーリエ変換
定式化
• 観測信号 は音源 と混合系 で表される
6
xij
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sij
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<latexit sha1_base64="t8MEfZYbT0ZY+e5m63yrdSh4/yU=">AAACgnichVHLSsNAFD2N9VUfrboR3BRLRVyUGxUUUSi6cdmHtYVaJImjBtMkJGlBS39At4oLVwouxL0/4MYfcNFPEJcKblx4mwZERb3DzJw5c8+dM1zVNnTXI2qFpK5wd09vX39kYHBoOBobGd10rZqjiYJmGZZTUhVXGLopCp7uGaJkO0KpqoYoqgdr7ftiXTiubpkb3qEtKlVlz9R3dU3xmMqubMcSlCI/4j+BHIAEgshYsTtsYQcWNNRQhYAJj7EBBS6PMmQQbOYqaDDnMNL9e4EmIqytcZbgDIXZA173+FQOWJPP7Zqur9b4FYOnw8o4kvRIN/RCD3RLT/T+a62GX6Pt5ZB3taMV9nb0eDz/9q+qyruH/U/Vn5497GLR96qzd9tn2r/QOvr60flLfimXbEzRFT2z/0tq0T3/wKy/atdZkbv4w4/KXprcHvl7M36CzdmUTCk5O59IrwaN6sMEJjHN3VhAGuvIoMDVBU5wijMpLM1IsjTXSZVCgWYMX0Ja/gBMl4+f</latexit>
<latexit sha1_base64="t8MEfZYbT0ZY+e5m63yrdSh4/yU=">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</latexit>
<latexit sha1_base64="t8MEfZYbT0ZY+e5m63yrdSh4/yU=">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</latexit>
0
B
B
B
@
ai,11 ai,12 . . . ai,1N
ai,21 ai,22 . . . ai,2N
.
.
.
.
.
.
...
.
.
.
ai,M1 ai,M2 . . . ai,MN
1
C
C
C
A
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xij
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Ai
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<latexit sha1_base64="zW58UJo6CA6GtarX8GLA1J+2Wzk=">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</latexit>
sij
<latexit sha1_base64="qH/3amT6CcnNprMfWtm/4gYvj9w=">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</latexit>
<latexit sha1_base64="qH/3amT6CcnNprMfWtm/4gYvj9w=">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</latexit>
<latexit sha1_base64="qH/3amT6CcnNprMfWtm/4gYvj9w=">AAACfnichVFNTxNBGH66KtYitOBF4qWxQLhQ3zUmNJyacPFIW1uatKTZXQY6dL+yO22om4a7f8CDJ02IISb6I7zwBzj0JxiPmHjhwNvtJkQJ8E5m5pln3uedZ2ZM35ahIhqntAcPH808Tj/JzD6dm8/mFhYbodcPLFG3PNsLmqYRClu6oq6kskXTD4ThmLbYMXtbk/2dgQhC6bnv1NAXu45x4Mp9aRmKqU5uqe2Y3lHUNj17zzFUN78cLo86kTwcdXIFKlIc+ZtAT0ABSWx7ua9oYw8eLPThQMCFYmzDQMitBR0En7ldRMwFjGS8LzBChrV9zhKcYTDb4/GAV62EdXk9qRnGaotPsbkHrMxjhc7plC7ojL7RL7q8tVYU15h4GfJsTrXC72Q/PK/9vVfl8KzQvVbd6VlhH6XYq2TvfsxMbmFN9YP3Hy9qm9WVaJW+0G/2/5nG9JNv4A7+WCcVUf2EDH+A/v9z3wSN10WdinrlTaG8lXxFGi/wEmv83hso4y22Uedzj3GC7/ihQVvV1rVX01QtlWie4Z/QSlfOUpNZ</latexit>
<latexit sha1_base64="qH/3amT6CcnNprMfWtm/4gYvj9w=">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</latexit>
: 周波数
: 時間
i = 1, 2, ..., I
<latexit sha1_base64="LIteWdwXVsX6RYh3l3jIuPy+HMY=">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</latexit>
<latexit sha1_base64="LIteWdwXVsX6RYh3l3jIuPy+HMY=">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</latexit>
<latexit sha1_base64="LIteWdwXVsX6RYh3l3jIuPy+HMY=">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</latexit>
<latexit sha1_base64="LIteWdwXVsX6RYh3l3jIuPy+HMY=">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</latexit>
j = 1, 2, ..., J
<latexit sha1_base64="brjlyaWUf9IPN1c2pQBT4mcLG/s=">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</latexit>
<latexit sha1_base64="brjlyaWUf9IPN1c2pQBT4mcLG/s=">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</latexit>
<latexit sha1_base64="brjlyaWUf9IPN1c2pQBT4mcLG/s=">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</latexit>
<latexit sha1_base64="brjlyaWUf9IPN1c2pQBT4mcLG/s=">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</latexit>
• 分離信号 は次式で表せる
yij = W ixij
<latexit sha1_base64="mrUXiMAWLEpQC+rVgkRlCYmW1Tw=">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</latexit>
<latexit sha1_base64="mrUXiMAWLEpQC+rVgkRlCYmW1Tw=">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</latexit>
<latexit sha1_base64="mrUXiMAWLEpQC+rVgkRlCYmW1Tw=">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</latexit>
<latexit sha1_base64="mrUXiMAWLEpQC+rVgkRlCYmW1Tw=">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</latexit>
yij
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<latexit sha1_base64="n46CIXNcW3hNWgV1DA60ajMlG/4=">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</latexit>
<latexit sha1_base64="n46CIXNcW3hNWgV1DA60ajMlG/4=">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</latexit>
<latexit sha1_base64="n46CIXNcW3hNWgV1DA60ajMlG/4=">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</latexit>
( )
Wi = A 1
i
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<latexit sha1_base64="F+MlsGj1T8OCxdDYfRUH1j7ZYE8=">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</latexit>
<latexit sha1_base64="F+MlsGj1T8OCxdDYfRUH1j7ZYE8=">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</latexit>
<latexit sha1_base64="F+MlsGj1T8OCxdDYfRUH1j7ZYE8=">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</latexit>
• BSSは分離行列 を全周波数で推定する最適化問題
Wi
<latexit sha1_base64="ZvHrIxNLcLk96c33DJSXsKTLRVU=">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</latexit>
<latexit sha1_base64="ZvHrIxNLcLk96c33DJSXsKTLRVU=">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</latexit>
<latexit sha1_base64="ZvHrIxNLcLk96c33DJSXsKTLRVU=">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</latexit>
<latexit sha1_base64="ZvHrIxNLcLk96c33DJSXsKTLRVU=">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</latexit>
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム
独立低ランク行列分析を用いたインタラクティブ音源分離システム

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  • 3. はじめに • ブラインド音源分離(BSS)は混合系が不明な観測信号か ら混合前の音源を推定する技術 • 独立成分分析(ICA)に基づく手法が発展してきた • 音源間の統計的独立性を最大化する音源分離手法 3 音源 観測信号 推定信号 Ai <latexit sha1_base64="zW58UJo6CA6GtarX8GLA1J+2Wzk=">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</latexit> <latexit 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sha1_base64="zW58UJo6CA6GtarX8GLA1J+2Wzk=">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</latexit> Wi <latexit sha1_base64="j/XMgTWefeddKZyEi0zX2ErO6do=">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</latexit> <latexit sha1_base64="j/XMgTWefeddKZyEi0zX2ErO6do=">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</latexit> <latexit sha1_base64="j/XMgTWefeddKZyEi0zX2ErO6do=">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</latexit> <latexit sha1_base64="j/XMgTWefeddKZyEi0zX2ErO6do=">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</latexit> 独立成分分析(ICA) [Comon, 1994] 周波数領域ICA(FDICA) [Smaragdis, 1998] 独立ベクトル分析(IVA) [Kim et al., 2006] 独立低ランク行列分析(ILRMA) [Kitamura et al., 2016] 多チャネル信号の ブラインド音源分離手法
  • 4. はじめに • 最新手法である独立低ランク行列分析(ILRMA)は音源 間の独立性に加えて,低ランク音源モデルを導入した反復 最適化アルゴリズム 4 ✓ <latexit sha1_base64="gTj/6LMVR0tepyfeQavNyvchgko=">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</latexit> f(✓) <latexit sha1_base64="pEd3WZr1D122pjTbon05bezJOOo=">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</latexit> ✓0 <latexit sha1_base64="4zcignHw1NFtJR8pzRyRdlxZOl8=">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</latexit> ✓0 <latexit sha1_base64="4zcignHw1NFtJR8pzRyRdlxZOl8=">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</latexit> 局所最適解 最適解 ユーザの介入 変数 目的関数
  • 5. 定式化 • 時間的に変化するスペクトルの表現 - 短時間フーリエ変換(short-time Fourier transform: STFT) 5 時間波形 … スペクトログラム 複素数要素を持つ行列 周波数 時間 … 時間領域 時間周波数領域 窓関数 シフト長 フーリエ変換長 離散フーリエ変換 離散フーリエ変換 離散フーリエ変換
  • 6. 定式化 • 観測信号 は音源 と混合系 で表される 6 xij <latexit sha1_base64="JQ0vvHrpCiqIy3k1G6lzvK+xD9E=">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</latexit> <latexit 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sha1_base64="brjlyaWUf9IPN1c2pQBT4mcLG/s=">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</latexit> • 分離信号 は次式で表せる yij = W ixij <latexit 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sha1_base64="mrUXiMAWLEpQC+rVgkRlCYmW1Tw=">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</latexit> yij <latexit 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