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

Kitamura Laboratory
Kitamura LaboratoryKitamura Laboratory
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=">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</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=">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</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=">AAACdXichVHLSsNAFD2N7/qKuhFECFbFRYk3IiiCUHAjrmy1KqiUJE41miYhSQu1+AP+gAvdKKiIn+HGH3DhJ4hLBTcuvE0DoqLeYWbOnLnnzpkZw7OtICR6TEhNzS2tbe0dyc6u7p5eua9/LXDLvinypmu7/oahB8K2HJEPrdAWG54v9JJhi3XjYKG+v14RfmC5zmpY9cR2Sd91rKJl6iFTBVneV+YVLT2VVlRVVdLKUkFOkUpRKD+BFoMU4lh25WtsYQcuTJRRgoCDkLENHQG3TWggeMxto8acz8iK9gWOkGRtmbMEZ+jMHvC4y6vNmHV4Xa8ZRGqTT7G5+6xUMEYPdEMvdE+39ETvv9aqRTXqXqo8Gw2t8Aq9x4Mrb/+qSjyH2PtU/ek5RBGzkVeLvXsRU7+F2dBXDk9eVuZyY7VxuqBn9n9Oj3THN3Aqr+ZlVuROkeQP0L4/90+wNqVqpGrZ6VRmNv6KdgxhBBP83jPIYBHLyPO5FZzhEleJN2lYGpXGG6lSItYM4EtIkx/X+o0/</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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Wi = A 1
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<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
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<latexit sha1_base64="ZvHrIxNLcLk96c33DJSXsKTLRVU=">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</latexit>
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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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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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