Inverse-Free Online Independent Vector Analysis With Flexible Iterative Source Steering

APSIPA 2022
WedAM1-8

Transcript

1. Inverse-free Online Independent Vector Analysis with
   Flexible Iterative Source Steering
   APSIPA ASC 2022
   WedAM1-8
   Taishi Nakashima Nobutaka Ono
   Tokyo Metropolitan University, Japan.
   9 November, 2022
   

   View Slide

2. Outline 1/13
   Problem
   • Online blind source separation
   � Essential for real-time applications
   Methods
   • Online auxiliary-function-based independent vector analysis (AuxIVA)
   � Good separation performance
   Purpose
   • To utilize iterative source steering (ISS) for online AuxIVA
   � To update one specific steering vector
   

   View Slide

3. Contents 2/13
   Introduction
   Conventional methods
   Frequency-domain BSS
   Batch AuxIVA
   Online AuxIVA
   Iterative source steering
   Proposed method: Online AuxIVA-ISS
   Experiment
   Conclusion
   

   View Slide

4. Multichannel blind source separation (BSS) 2/13
   Blind
   Source
   Separation
   • To recover source signals from observed signals
   

   View Slide

5. Multichannel blind source separation (BSS) 2/13
   Blind
   Source
   Separation
   • To recover source signals from observed signals
   

   View Slide

6. Multichannel blind source separation (BSS) 2/13
   Blind
   Source
   Separation
   • To recover source signals from observed signals
   

   View Slide

7. Multichannel blind source separation (BSS) 2/13
   Blind
   Source
   Separation
   Observed
   • To recover source signals from observed signals
   

   View Slide

8. Multichannel blind source separation (BSS) 2/13
   Observed Estimated
   Blind
   Source
   Separation
   • To recover source signals from observed signals
   

   View Slide

9. Multichannel blind source separation (BSS) 2/13
   Observed Estimated
   Blind
   Source
   Separation
   • To recover source signals from observed signals
   🎺🎸🎹
   

   View Slide

10. Contents 3/13
    Introduction
    Conventional methods
    Frequency-domain BSS
    Batch AuxIVA
    Online AuxIVA
    Iterative source steering
    Proposed method: Online AuxIVA-ISS
    Experiment
    Conclusion
    

    View Slide

11. Frequency-domain BSS 3/13
    .
    .
    .
    Mix. system Demix. system Estimated
    Observed
    Source
    freq.
    time
    src.
    .
    .
    .
    Mixing system
    Observed
    𝒙𝑓𝑡
    =
    Mixing matrix
    𝑨𝑓
    𝒔𝑓𝑡
    Demixing system
    Estimated
    𝒚𝑓𝑡
    =
    Demixing matrix
    𝑾𝑓
    𝒙𝑓𝑡
    

    View Slide

12. Frequency-domain BSS 3/13
    .
    .
    .
    Mix. system Demix. system Estimated
    Observed
    Source
    freq.
    time
    src.
    .
    .
    .
    Mixing system
    Observed
    𝒙𝑓𝑡
    =
    Mixing matrix
    𝑨𝑓
    𝒔𝑓𝑡
    Demixing system
    Estimated
    𝒚𝑓𝑡
    =
    Demixing matrix
    𝑾𝑓
    𝒙𝑓𝑡
    Goal
    To estimate 𝑾𝑓
    such that 𝒚𝑓𝑡
    approximates 𝒔𝑓𝑡
    

    View Slide

13. Batch vs online 4/13
    Estimated
    Observed
    Blind
    Source
    Separation
    Batch BSS
    � High separation performance
    � Weak against dynamic environment
    � Inappropriate for real-time
    Online BSS
    � Robust against dynamic environment
    � Limited separation performance
    � Complex parameter tuning
    

    View Slide

14. Batch vs online 4/13
    Estimated
    Observed
    Blind
    Source
    Separation
    Batch BSS
    � High separation performance
    � Weak against dynamic environment
    � Inappropriate for real-time
    Online BSS
    � Robust against dynamic environment
    � Limited separation performance
    � Complex parameter tuning
    

    View Slide

15. Batch vs online 4/13
    Estimated
    Observed
    Blind
    Source
    Separation
    Batch BSS
    � High separation performance
    � Weak against dynamic environment
    � Inappropriate for real-time
    Online BSS
    � Robust against dynamic environment
    � Limited separation performance
    � Complex parameter tuning
    

    View Slide

16. Batch vs online 4/13
    Estimated
    Observed
    Blind
    Source
    Separation
    Batch BSS
    � High separation performance
    � Weak against dynamic environment
    � Inappropriate for real-time
    Online BSS
    � Robust against dynamic environment
    � Limited separation performance
    � Complex parameter tuning
    

    View Slide

17. Batch vs online 4/13
    Estimated
    Observed
    Blind
    Source
    Separation
    Batch BSS
    � High separation performance
    � Weak against dynamic environment
    � Inappropriate for real-time
    Online BSS
    � Robust against dynamic environment
    � Limited separation performance
    � Complex parameter tuning
    

    View Slide

18. Batch AuxIVA [Ono2011]
    5/13
    Auxiliary function for IVA
    min. 𝐽+({𝑾𝑓
    }𝑓
    ) = ∑
    𝑓
    [−2 log|det
    Parameter
    𝑾𝑓
    | + ∑
    𝑘
    𝒘H
    𝑘𝑓
    𝑼𝑘𝑓
    Parameter
    𝒘𝑘𝑓
    ]
    where 𝑼𝑘𝑓
    =
    1
    𝑇
    𝑇
    ∑
    𝑡=1
    𝒙𝑓𝑡
    𝒙H
    𝑓𝑡
    2𝑟𝑘𝑓𝑡
    

    View Slide

19. Batch AuxIVA [Ono2011]
    5/13
    Auxiliary function for IVA
    min. 𝐽+({𝑾𝑓
    }𝑓
    ) = ∑
    𝑓
    [−2 log|det
    Parameter
    𝑾𝑓
    | + ∑
    𝑘
    𝒘H
    𝑘𝑓
    𝑼𝑘𝑓
    Parameter
    𝒘𝑘𝑓
    ]
    where 𝑼𝑘𝑓
    =
    1
    𝑇
    𝑇
    ∑
    𝑡=1
    𝒙𝑓𝑡
    𝒙H
    𝑓𝑡
    2𝑟𝑘𝑓𝑡
    Iterative projection (IP) [Ono2011]
    • To minimize 𝐽+ w.r.t. 𝑾𝑓
    𝒘𝑘𝑓
    ← (𝑾𝑓
    𝑼𝑘𝑓
    )−1𝒆𝑘
    𝒘𝑘𝑓
    ←
    𝒘𝑘𝑓
    √𝒘H
    𝑘𝑓
    𝑼𝑘𝑓
    𝒘𝑘𝑓
    

    View Slide

20. Batch AuxIVA [Ono2011]
    5/13
    Auxiliary function for IVA
    min. 𝐽+({𝑾𝑓
    }𝑓
    ) = ∑
    𝑓
    [−2 log|det 𝑾𝑓
    | + ∑
    𝑘
    𝒘H
    𝑘𝑓
    𝑼𝑘𝑓
    𝒘𝑘𝑓
    ]
    where 𝑼𝑘𝑓
    =
    1
    𝑇
    𝑇
    ∑
    𝑡=1
    𝒙𝑓𝑡
    𝒙H
    𝑓𝑡
    2𝑟𝑘𝑓𝑡
    Iterative projection (IP) [Ono2011]
    • To minimize 𝐽+ w.r.t. 𝑾𝑓
    𝒘𝑘𝑓
    ← (𝑾𝑓
    𝑼𝑘𝑓
    )−1𝒆𝑘
    𝒘𝑘𝑓
    ←
    𝒘𝑘𝑓
    √𝒘H
    𝑘𝑓
    𝑼𝑘𝑓
    𝒘𝑘𝑓
    � Requires observed signals 𝒙𝑓𝑡
    for all 𝑡 to calculate 𝑼𝑘𝑓
    

    View Slide

21. Online AuxIVA [Taniguchi+2014]
    6/13
    Modification of signal model
    𝒙𝑓𝑡
    =
    Time-variant
    𝑨𝑓𝑡
    𝒔𝑓𝑡
    𝒚𝑓𝑡
    = 𝑾𝑓𝑡
    𝒙𝑓𝑡
    Incremental update of covariance matrices
    𝑼𝑘𝑓𝑡
    ←
    Forgetting factor (0 < 𝛼 ≤ 1)
    𝛼
    Past data
    𝑼𝑘𝑓(𝑡−1)
    + (1 − 𝛼)
    Current data
    1
    2𝑟𝑘𝑡
    𝒙𝑓𝑡
    𝒙H
    𝑓𝑡
    

    View Slide

22. Online AuxIVA [Taniguchi+2014]
    6/13
    Modification of signal model
    𝒙𝑓𝑡
    =
    Time-variant
    𝑨𝑓𝑡
    𝒔𝑓𝑡
    𝒚𝑓𝑡
    = 𝑾𝑓𝑡
    𝒙𝑓𝑡
    Incremental update of covariance matrices
    𝑼𝑘𝑓𝑡
    ←
    Forgetting factor (0 < 𝛼 ≤ 1)
    𝛼
    Past data
    𝑼𝑘𝑓(𝑡−1)
    + (1 − 𝛼)
    Current data
    1
    2𝑟𝑘𝑡
    𝒙𝑓𝑡
    𝒙H
    𝑓𝑡
    Motivation
    • To update 𝑾𝑓𝑡
    efficiently
    ∘ 𝑾𝑓𝑡
    should converge after sufficient frames
    

    View Slide

23. Online AuxIVA [Taniguchi+2014]
    6/13
    Modification of signal model
    𝒙𝑓𝑡
    =
    Time-variant
    𝑨𝑓𝑡
    𝒔𝑓𝑡
    𝒚𝑓𝑡
    = 𝑾𝑓𝑡
    𝒙𝑓𝑡
    Incremental update of covariance matrices
    𝑼𝑘𝑓𝑡
    ←
    Forgetting factor (0 < 𝛼 ≤ 1)
    𝛼
    Past data
    𝑼𝑘𝑓(𝑡−1)
    + (1 − 𝛼)
    Current data
    1
    2𝑟𝑘𝑡
    𝒙𝑓𝑡
    𝒙H
    𝑓𝑡
    Motivation
    • To update 𝑾𝑓𝑡
    efficiently
    ∘ 𝑾𝑓𝑡
    should converge after sufficient frames
    � Exploit property of iterative source steering
    

    View Slide

24. Iterative source steering (ISS) [Scheibler+2020]
    7/13
    • Update rule of 𝑾𝑓
    using elementary row operations
    𝑾𝑓
    ← 𝑾𝑓
    − 𝒗𝑘𝑓
    𝒘H
    𝑘𝑓
    𝑣𝑚𝑘𝑓
    =
    ⎧
    {
    ⎨
    {
    ⎩
    𝒘H
    𝑚𝑓
    𝑼𝑚𝑓
    𝒘𝑘𝑓
    𝒘H
    𝑘𝑓
    𝑼𝑚𝑓
    𝒘
    𝑘𝑓
    (if 𝑚 ≠ 𝑘)
    1 − (𝒘H
    𝑘𝑓
    𝑼𝑘𝑓
    𝒘𝑘𝑓
    )−1
    2 (if 𝑚 = 𝑘)
    � Inverse-free
    

    View Slide

25. Intuitive interpretation of ISS 8/13
    • Equivalent to updates of steering vectors 𝒂𝑘𝑓
    [Scheibler+2020]
    𝒂𝑘𝑓
    ← 1
    1−𝑣𝑘𝑘𝑓
    (𝒂𝑘𝑓
    + ∑
    𝑚≠𝑘
    𝑣𝑚𝑘𝑓
    𝒂𝑚𝑓
    )
    

    View Slide

26. Intuitive interpretation of ISS 8/13
    • Equivalent to updates of steering vectors 𝒂𝑘𝑓
    [Scheibler+2020]
    𝒂𝑘𝑓
    ← 1
    1−𝑣𝑘𝑘𝑓
    (𝒂𝑘𝑓
    + ∑
    𝑚≠𝑘
    𝑣𝑚𝑘𝑓
    𝒂𝑚𝑓
    )
    

    View Slide

27. Intuitive interpretation of ISS 8/13
    • Equivalent to updates of steering vectors 𝒂𝑘𝑓
    [Scheibler+2020]
    𝒂𝑘𝑓
    ← 1
    1−𝑣𝑘𝑘𝑓
    (𝒂𝑘𝑓
    + ∑
    𝑚≠𝑘
    𝑣𝑚𝑘𝑓
    𝒂𝑚𝑓
    )
    � Example: after source 𝑠1𝑓𝑡
    moves...
    

    View Slide

28. Intuitive interpretation of ISS 8/13
    • Equivalent to updates of steering vectors 𝒂𝑘𝑓
    [Scheibler+2020]
    𝒂𝑘𝑓
    ← 1
    1−𝑣𝑘𝑘𝑓
    (𝒂𝑘𝑓
    + ∑
    𝑚≠𝑘
    𝑣𝑚𝑘𝑓
    𝒂𝑚𝑓
    )
    � Example: after source 𝑠1𝑓𝑡
    moves...
    � IP: update 𝒘2𝑓𝑡
    , 𝒘3𝑓𝑡
    , …
    

    View Slide

29. Intuitive interpretation of ISS 8/13
    • Equivalent to updates of steering vectors 𝒂𝑘𝑓
    [Scheibler+2020]
    𝒂𝑘𝑓
    ← 1
    1−𝑣𝑘𝑘𝑓
    (𝒂𝑘𝑓
    + ∑
    𝑚≠𝑘
    𝑣𝑚𝑘𝑓
    𝒂𝑚𝑓
    )
    � Example: after source 𝑠1𝑓𝑡
    moves...
    � IP: update 𝒘2𝑓𝑡
    , 𝒘3𝑓𝑡
    , …
    � ISS: update only 𝒂1𝑓𝑡
    

    View Slide

30. Contents 9/13
    Introduction
    Conventional methods
    Frequency-domain BSS
    Batch AuxIVA
    Online AuxIVA
    Iterative source steering
    Proposed method: Online AuxIVA-ISS
    Experiment
    Conclusion
    

    View Slide

31. Online AuxIVA with ISSPROPOSED
    9/13
    for 𝑡 = 1, … , 𝑇 do
    𝑾𝑓𝑡
    ← 𝑾𝑓(𝑡−1)
    (∀𝑓)
    for it = 1, … , 𝑁it
    do
    for 𝑘 = 1, … , 𝐾 do
    𝑟𝑘𝑡
    ← √∑
    𝑓
    |𝒘H
    𝑘𝑓𝑡
    𝒙𝑓𝑡
    |2
    𝑼𝑘𝑓𝑡
    ← 𝛼𝑼𝑘𝑓(𝑡−1)
    + (1 − 𝛼) 1
    2𝑟𝑘𝑡
    𝒙𝑓𝑡
    𝒙H
    𝑓𝑡
    (∀𝑓)
    for 𝑘 ∈ 𝒦 do
    for 𝑚 = 1, … , 𝐾 do
    𝑣𝑚𝑘𝑓
    ←
    ⎧
    {
    ⎨
    {
    ⎩
    𝒘H
    𝑚𝑓
    𝑼𝑚𝑓
    𝒘𝑘𝑓
    𝒘H
    𝑘𝑓
    𝑼𝑚𝑓
    𝒘
    𝑘𝑓
    if 𝑚 ≠ 𝑘
    1 − (𝒘H
    𝑘𝑓
    𝑼𝑘𝑓
    𝒘𝑘𝑓
    )−1
    2 if 𝑚 = 𝑘
    (∀𝑓)
    𝑾𝑓𝑡
    ← 𝑾𝑓𝑡
    − 𝒗𝑘𝑓
    𝒘H
    𝑘𝑓𝑡
    (∀𝑓)
    𝒚𝑓𝑡
    = 𝑾𝑓𝑡
    𝒙𝑓𝑡
    (∀𝑓)
    

    View Slide

32. Online AuxIVA with ISSPROPOSED
    9/13
    for 𝑡 = 1, … , 𝑇 do
    𝑾𝑓𝑡
    ← 𝑾𝑓(𝑡−1)
    (∀𝑓)
    for it = 1, … , 𝑁it
    do
    for 𝑘 = 1, … , 𝐾 do
    𝑟𝑘𝑡
    ← √∑
    𝑓
    |𝒘H
    𝑘𝑓𝑡
    𝒙𝑓𝑡
    |2
    𝑼𝑘𝑓𝑡
    ← 𝛼𝑼𝑘𝑓(𝑡−1)
    + (1 − 𝛼) 1
    2𝑟𝑘𝑡
    𝒙𝑓𝑡
    𝒙H
    𝑓𝑡
    (∀𝑓)
    for
    Source index set to be udpated
    𝑘 ∈ 𝒦 do
    for 𝑚 = 1, … , 𝐾 do
    𝑣𝑚𝑘𝑓
    ←
    ⎧
    {
    ⎨
    {
    ⎩
    𝒘H
    𝑚𝑓
    𝑼𝑚𝑓
    𝒘𝑘𝑓
    𝒘H
    𝑘𝑓
    𝑼𝑚𝑓
    𝒘
    𝑘𝑓
    if 𝑚 ≠ 𝑘
    1 − (𝒘H
    𝑘𝑓
    𝑼𝑘𝑓
    𝒘𝑘𝑓
    )−1
    2 if 𝑚 = 𝑘
    (∀𝑓)
    𝑾𝑓𝑡
    ← 𝑾𝑓𝑡
    − 𝒗𝑘𝑓
    𝒘H
    𝑘𝑓𝑡
    (∀𝑓)
    𝒚𝑓𝑡
    = 𝑾𝑓𝑡
    𝒙𝑓𝑡
    (∀𝑓)
    

    View Slide

33. Online AuxIVA with ISSPROPOSED
    9/13
    for 𝑡 = 1, … , 𝑇 do
    𝑾𝑓𝑡
    ← 𝑾𝑓(𝑡−1)
    (∀𝑓)
    for it = 1, … , 𝑁it
    do
    for 𝑘 = 1, … , 𝐾 do
    𝑟𝑘𝑡
    ← √∑
    𝑓
    |𝒘H
    𝑘𝑓𝑡
    𝒙𝑓𝑡
    |2
    𝑼𝑘𝑓𝑡
    ← 𝛼𝑼𝑘𝑓(𝑡−1)
    + (1 − 𝛼) 1
    2𝑟𝑘𝑡
    𝒙𝑓𝑡
    𝒙H
    𝑓𝑡
    (∀𝑓)
    for
    Source index set to be udpated
    Example:
    Until 𝑾𝑓𝑡
    converge 𝒦 = {1, … , 𝐾}
    After 𝑾𝑓𝑡
    converge 𝒦 = ∅
    When source 𝑙 moves 𝒦 = {𝑙}
    𝑘 ∈ 𝒦 do
    for 𝑚 = 1, … , 𝐾 do
    𝑣𝑚𝑘𝑓
    ←
    ⎧
    {
    ⎨
    {
    ⎩
    𝒘H
    𝑚𝑓
    𝑼𝑚𝑓
    𝒘𝑘𝑓
    𝒘H
    𝑘𝑓
    𝑼𝑚𝑓
    𝒘
    𝑘𝑓
    if 𝑚 ≠ 𝑘
    1 − (𝒘H
    𝑘𝑓
    𝑼𝑘𝑓
    𝒘𝑘𝑓
    )−1
    2 if 𝑚 = 𝑘
    (∀𝑓)
    𝑾𝑓𝑡
    ← 𝑾𝑓𝑡
    − 𝒗𝑘𝑓
    𝒘H
    𝑘𝑓𝑡
    (∀𝑓)
    𝒚𝑓𝑡
    = 𝑾𝑓𝑡
    𝒙𝑓𝑡
    (∀𝑓)
    

    View Slide

34. Contents 10/13
    Introduction
    Conventional methods
    Frequency-domain BSS
    Batch AuxIVA
    Online AuxIVA
    Iterative source steering
    Proposed method: Online AuxIVA-ISS
    Experiment
    Conclusion
    

    View Slide

35. Setup 10/13
    Room layout
    Width = �.� m
    Depth = �.� m
    �
    �
    �
    Height = �.�� m
    Microphones
    Source (fixed)
    Source (moved)
    

    View Slide

36. Setup 10/13
    Room layout
    Width = �.� m
    Depth = �.� m
    �
    �
    �
    �`
    Height = �.�� m
    Microphones
    Source (fixed)
    Source (moved)
    1. Copy source 3 to source 3′
    

    View Slide

37. Setup 10/13
    Room layout
    Width = �.� m
    Depth = �.� m
    �
    �
    �
    �`
    Height = �.�� m
    Microphones
    Source (fixed)
    Source (moved)
    1. Copy source 3 to source 3′
    2. Cut second half of source 3
    Cut first half of source 3′
    

    View Slide

38. Setup 10/13
    Room layout
    Width = �.� m
    Depth = �.� m
    �
    �
    �
    �`
    Height = �.�� m
    Microphones
    Source (fixed)
    Source (moved)
    1. Copy source 3 to source 3′
    2. Cut second half of source 3
    Cut first half of source 3′
    � Instant movement of the source 3
    

    View Slide

39. Setup 10/13
    Room layout
    Width = �.� m
    Depth = �.� m
    �
    �
    �
    �`
    Height = �.�� m
    Microphones
    Source (fixed)
    Source (moved)
    1. Copy source 3 to source 3′
    2. Cut second half of source 3
    Cut first half of source 3′
    � Instant movement of the source 3
    Methods
    Name Target source indices 𝒦
    Before move After move
    🆕 ISS-all {1, 2, 3} {1, 2, 3}
    🆕 ISS-one {1, 2, 3} {3}
    IP-all {1, 2, 3} {1, 2, 3}
    IP-one {1, 2, 3} {3}
    

    View Slide

40. Setup 10/13
    Room layout
    Width = �.� m
    Depth = �.� m
    �
    �
    �
    �`
    Height = �.�� m
    Microphones
    Source (fixed)
    Source (moved)
    1. Copy source 3 to source 3′
    2. Cut second half of source 3
    Cut first half of source 3′
    � Instant movement of the source 3
    Methods
    Name Target source indices 𝒦
    Before move After move
    🆕 ISS-all {1, 2, 3} {1, 2, 3}
    🆕 ISS-one {1, 2, 3} {3}
    IP-all {1, 2, 3} {1, 2, 3}
    IP-one {1, 2, 3} {3}
    Note
    When and which source moves is
    known as an oracle in this experiment
    

    View Slide

41. Separation performance 11/13
    0
    20
    ISS-all ISS-one IP-all IP-one
    0
    20
    0 5 10 15 20 25 30
    Segment index
    0
    20
    SegSDR improvement (dB)
    $I
    $I
    $I
    $I
    $I
    $I
    • Segmental SDR improvements by channels
    

    View Slide

42. Separation performance 11/13
    0
    20
    ISS-all ISS-one IP-all IP-one
    0
    20
    0 5 10 15 20 25 30
    Segment index
    0
    20
    Source 3 moved
    SegSDR improvement (dB)
    $I
    $I
    $I
    $I
    $I
    $I
    • Vertical dashed line indicates movement of source 3
    

    View Slide

43. Separation performance 11/13
    0
    20
    ISS-all ISS-one IP-all IP-one
    0
    20
    0 5 10 15 20 25 30
    Segment index
    0
    20
    Source 3 moved
    SegSDR improvement (dB)
    $I
    $I
    $I
    $I
    $I
    $I
    • Before source 3 moved: update demixing matrices for all source indices
    

    View Slide

44. Separation performance 11/13
    0
    20
    ISS-all ISS-one IP-all IP-one
    0
    20
    0 5 10 15 20 25 30
    Segment index
    0
    20
    Source 3 moved
    SegSDR improvement (dB)
    $I
    $I
    $I
    $I
    $I
    $I
    • After source 3 moved: ISS-one updates only 𝒂3𝑓
    , IP-one updates only 𝒘3𝑓
    

    View Slide

45. Separation performance 11/13
    0
    20
    ISS-all ISS-one IP-all IP-one
    0
    20
    0 5 10 15 20 25 30
    Segment index
    0
    20
    Source 3 moved
    SegSDR improvement (dB)
    $I
    $I
    $I
    $I
    $I
    $I
    • Degraded separation performance due to moving source
    

    View Slide

46. Separation performance 11/13
    0
    20
    ISS-all ISS-one IP-all IP-one
    0
    20
    0 5 10 15 20 25 30
    Segment index
    0
    20
    Source 3 moved
    SegSDR improvement (dB)
    $I
    $I
    $I
    $I
    $I
    $I
    • Steadily improved thanks to online updates
    

    View Slide

47. Separation performance 11/13
    0
    20
    ISS-all ISS-one IP-all IP-one
    0
    20
    0 5 10 15 20 25 30
    Segment index
    0
    20
    Source 3 moved
    SegSDR improvement (dB)
    $I
    $I
    $I
    $I
    $I
    $I
    � ISS-one : almost the same performance as ISS-all with less updates
    

    View Slide

48. Separation performance 11/13
    0
    20
    ISS-all ISS-one IP-all IP-one
    0
    20
    0 5 10 15 20 25 30
    Segment index
    0
    20
    Source 3 moved
    SegSDR improvement (dB)
    $I
    $I
    $I
    $I
    $I
    $I
    � ISS-one : higher performance than IP-one
    

    View Slide

49. Runtime 12/13
    IP-all ISS-all ISS-one
    0
    2
    4
    6
    8
    10
    12
    Runtime (s)
    11.54
    11.00
    8.66
    � ISS-one was faster than IP-all
    

    View Slide

50. Contents 13/13
    Introduction
    Conventional methods
    Frequency-domain BSS
    Batch AuxIVA
    Online AuxIVA
    Iterative source steering
    Proposed method: Online AuxIVA-ISS
    Experiment
    Conclusion
    

    View Slide

51. Conclusion 13/13
    Summary
    • New online AuxIVA with iterative source steering (ISS)
    � Good separation performance under dynamic environment
    � Efficient update when the single source moves
    

    View Slide

52. Conclusion 13/13
    Summary
    • New online AuxIVA with iterative source steering (ISS)
    � Good separation performance under dynamic environment
    � Efficient update when the single source moves
    Future work
    • Automatic detection of moveing sources
    • Efficient forgetting factor tuning
    • Efficient update rule of ISS
    

    View Slide

53. References i
    [Ono2011] N. Ono, “Stable and fast update rules for independent vector analysis based on auxiliary function
    technique,” in Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and
    Acoustics (WASPAA), pp. 189–192, 2011.
    [Scheibler+2020] R. Scheibler and N. Ono, “Fast and stable blind source separation with rank-1 updates,” in
    Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May
    2020.
    [Taniguchi+2014] T. Taniguchi, N. Ono, A. Kawamura, and S. Sagayama, “An auxiliary-function approach to online
    independent vector analysis for real-time blind source separation,” in Proceedings of Hands-Free
    Speech Communication and Microphone Arrays (HSCMA), pp. 107–111, May 2014.
    Thank you!
    

    View Slide