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Introduction of our research (FY2021)

Introduction of our research (FY2021)

Beeb4cfb45c3fa586526aa131ea67683?s=128

Shoichi Koyama

March 23, 2021
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  1. Introduction of Our Research on Sound Field Analysis and Control

    in FY2021 Shoichi Koyama, Ph.D. The University of Tokyo
  2. Analysis and control of acoustic field March 23, 2021 2

    Analysis Control Ø Visualization and reconstruction of acoustic field Ø Estimation of source locations and room-acoustic parameters Ø Spatial sound field recording Ø High-fidelity spatial audio reproduction Ø Directivity control and local reproduction Ø Spatial active noise control From theory to application of signal processing and inverse problems for acoustic fields Microphone Loudspeaker
  3. Summary in sound field analysis March 23, 2021 3 •

    Sound field reconstruction based on harmonic analysis of infinite order [Ueno+ IEEE SPL 2018] • Optimization algorithm for sparse representation of acoustic field [Murata+ IEEE TSP 2018] • Sparse sound field decomposition in reverberant environment [Koyama+ IEEE JSTSP 2019] • Separation of internal and external sound fields [Takida+ EUSIPCO 2018] • Estimation of source parameters based on Reciprocity Gap Functional [Takida+ Elsevier SP 2019] Analysis inside region without sources Analysis inside region including sources Target region Target region
  4. Summary in sound field control March 23, 2021 4 •

    Sound field control based on weighted mode-matching [Ueno+ IEEE/ACM TASLP 2019] • Sound field recording and reproduction in wave-number domain [Koyama+ IEEE(/ACM) TASLP 2013, 2014, JASA 2016] • Super-resolution in recording and reproduction [Koyama+ IEEE JSTSP 2015, JASA 2018] • Optimization of source and sensor placement for sound field control [Koyama+ IEEE/ACM TASLP 2020, IEEE ICASSP 2018] • Spatial active noise control based on kernel interpolation [Ito+ IEEE ICASSP 2019]
  5. SOUND FIELD ANALYSIS March 23, 2021 5

  6. Analysis inside region without sources March 23, 2021 6 Ø

    Sound field satisfies homogeneous Helmholtz eq. <latexit sha1_base64="U/XXJXKvIw2E1EilpsiBLtz7MGo=">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</latexit> <latexit sha1_base64="okEXIY/pPSAfenmSSDCRtw4HgOI=">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</latexit> Microphone Sound wave Unknown boundary condition outside <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit> Expansion into finite number of plane waves / spherical harmonics is typical approach
  7. Analysis inside region without sources Ø Spherical wavefunction expansion Ø

    Estimation of expansion coeff at arbitrary point March 23, 2021 7 [Ueno+ IEEE SPL 2018] <latexit sha1_base64="TnKjsQx5LCjG+RPMUHDUz7skgmU=">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</latexit> Spherical wavefunction Expansion coeff at center <latexit sha1_base64="D9HWprNBRjV9vUhnlaU3sm3abQc=">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</latexit> <latexit sha1_base64="8B+ZNBL5UQkvn4J1WUEojaP77iI=">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</latexit> Estimates of expansion coeff at <latexit sha1_base64="8B+ZNBL5UQkvn4J1WUEojaP77iI=">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</latexit> Matrix product of infinite orders can be analytically derived, and dependency on expansion center is eliminated Observations <latexit 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sha1_base64="PC9pAlu3s2zNT+S7GE8ISzdeo94=">AAADYHicdZJLixNBEIB7Mz5ifOxGb3oZDIKnMOMKehHCevGysILZDWRCqOnUJE36MXTX7CYO8Ud41T/m1V9iTzarZjMpaCi+qo/qbirNpXAURb8OGsGdu/fuNx+0Hj56/OTwqP303JnCcuxzI40dpOBQCo19EiRxkFsElUq8SOcfq/rFJVonjP5CyxxHCqZaZIIDeTRIUlXa1TgaH3WibrSOcDeJN0mHbeJs3G6cJBPDC4WauATnhnGU06gES4JLXLWSwmEOfA5THPpUg0I3KtcXXoWvPJmEmbH+aArX9H+jBOXcUqW+UwHN3O1aBetqw4Ky96NS6Lwg1Px6UFbIkExYvT6cCIuc5NInwK3wdw35DCxw8n+0NSVV/g0ar7hRCvSkTMBOFSxWZVJNNXmZWBV69q2CiRRKkKsxhK4xPNxruCLfNSq41xA62zUqWG/46R5/xW3nL90jwaJOuqH/JAVzBL+F5D+0lfDeKSxOgaxY+FV0H+Ljmw5DM7R+6+LbO7abnL/pxlE3/vy20zvZ7F+TvWAv2WsWs3esxz6xM9ZnnEn2nf1gPxu/g2ZwGLSvWxsHG+cZ24rg+R+OnyK8</latexit> Matrix of translation operators <latexit sha1_base64="PC9pAlu3s2zNT+S7GE8ISzdeo94=">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</latexit>
  8. Relation to kernel ridge regression Ø Corresponds to kernel ridge

    regression using spherical Bessel function as kernel function March 23, 2021 8 [Ueno+ IEEE SPL 2018, IWAENC 2018] <latexit sha1_base64="Nwb3n7CEyAyxNvvm5JH9L1bryVs=">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</latexit> Gram matrix consisting of spherical Bessel functions Observations Position of th mic <latexit sha1_base64="0uStd8PEwCtmctIFyVxU/PU2PFc=">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</latexit> Kernel ridge regression with constraint that interpolation function satisfies Helmholtz eq. <latexit sha1_base64="E0VINkcXCNAwA1Jtzy3Bn53aBRg=">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</latexit>
  9. Results of simulation experiments March 23, 2021 9 Proposed Proposed

    Gaussian kernel Error Ø Reconstruction of sound field generated by single loudspeaker • 18 mics, low-pass pulse signal True
  10. Application to binaural rendering Ø Binaural reproduction from mic array

    signals March 23, 2021 10 Recording Reproduction Signal conversion Ø Binaural reproduction at arbitrary listening position from distributed mic signals • Efficiently capturing broad area of sound field • Flexible mic array configuration [Iijima+ IEEE MMSP 2020]
  11. Application to binaural rendering Ø Estimate expansion coefs in recording

    area Ø Binaural signals are synthesized by weighted integral of HRTFs March 23, 2021 11 Spherical wavefunc HRTF Expansion coef of HRTF Weight for HRTF is estimated by harmonic analysis of infinite order Conversion from distributed mic signals to binaural signals [Iijima+ IEEE MMSP 2020]
  12. Application to binaural rendering Ø Demo system consisting of 8

    small mic arrays and 360- degree camera March 23, 2021 12 Proposed Single array Binaural reproduction error distribution § Large area of high reproduction accuracy § Suitable for tracking head translation and rotation (3DoF → 6DoF)
  13. Application to spatial ANC Ø Active Noise Control: ANC –

    Noise cancellation using adaptive filter and loudspeaker Ø Noise control at discrete positions in conventional method March 23, 2021 13 ANC inside continuous region: spatial ANC [Ito+ IEEE ICASSP 2019]
  14. Application to spatial ANC Ø Cost function is formulated as

    regional noise power which is estimated by using kernel interpolation method for acoustic field March 23, 2021 14 <latexit sha1_base64="8sG3MC3lrsBMuNZaKxR7z4Tos08=">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</latexit> <latexit sha1_base64="Xjw/jwTwxeAj54v/lgakjUqgUCg=">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</latexit> Gram matrix for sound field interpolation Kernel function for sound field interpolation Regional noise power Weighting matrix determined only by kernel funcs Ø Not only on discrete points, but regional noise control. Ø Computational cost for filter update is equivalent to conventional method [Ito+ IEEE ICASSP 2019]
  15. Application to spatial ANC Ø ANC based on weighted normalized

    least mean square (NLMS) as adaptive filter March 23, 2021 15 Noise source Reference mic Secondary path Error mic Weighted NLMS Adaptive filter <latexit sha1_base64="6jxgo/ZFQN4grGNTy6hJW6mkfw8=">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</latexit> <latexit sha1_base64="gZ4y0s+Ju4HTfczPeU9lR8uUGGM=">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</latexit> <latexit sha1_base64="p08G7F0QTz8++Zfa7RXJ2cJdAGo=">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</latexit> <latexit sha1_base64="cd2ZPdzJsne9Qg0zaED0AnVkuHg=">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</latexit> <latexit sha1_base64="RCYKXy3tAXaKbjqf0uxQlC+5rBg=">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</latexit> Driving signals <latexit sha1_base64="fUoTzLAXQTCGuzUzainTxTdFqRg=">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</latexit> Cost function: Filter update: Power of error mic including weighting coeff <latexit sha1_base64="eK62SxlrjP6i2nyGxlFlB6zwMj0=">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</latexit> <latexit sha1_base64="zanf4fTgx+iNYFFPFxKmlWRqETc=">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</latexit>
  16. Results of simulation experiment Ø Reduction of noise from three

    sources March 23, 2021 16 Proposed Conventional (multipoint control) Power dist. Regional noise reduction is achieved by proposed method [Ito+ IEEE ICASSP 2019] -6.2 dB -10.5 dB
  17. Analysis inside region including sources March 23, 2021 17 Ø

    Sound field satisfies inhomogeneous Helmholtz eq. Source Microphone Reflected wave <latexit sha1_base64="VXB56x8cV3M2DCu+b66chBSNCqQ=">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</latexit> Unknown boundary condition outside <latexit sha1_base64="okEXIY/pPSAfenmSSDCRtw4HgOI=">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</latexit> Source distribution <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit> This ill-posed inverse problem requires some constraint on source distribution for reconstruction
  18. Sparse sound field decomposition Ø Summation of particular and homogeneous

    solutions Ø Discretizing region leads to linear equation March 23, 2021 18 <latexit sha1_base64="reMY8i1ewjRGRTHn33uoP6JqdRU=">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</latexit> Grid point [Koyama+ ICASSP 2014] Free-field Green’s func : Dictionary matrix : Observations : Direct source component : reverberant component
  19. Sparse sound field decomposition Ø Assume that source distribution is

    spatially sparse and reconstruct sound field from observations Ø Group sparsity in time-frequency domain can also be taken into consideration March 23, 2021 19 <latexit sha1_base64="3unqeYcLzapR+kwzDMNoEVC+dbw=">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</latexit> <latexit sha1_base64="KdqboG5ErTF8Tsp8xTcQLhLEdoY=">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</latexit> Sparsity-inducing penalty term Non-zero grid point <latexit sha1_base64="CMp0bdMsbHJXrQaEDWLvT3oAJJo=">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</latexit> <latexit sha1_base64="f0AM1dFjbF0IvWOeeDQ4Zux15bE=">AAADWXicdZLNattAEIDXVtu47l/SHHMRNYWejNQG2kvApJdcAgnEScAyYbQe2Yv3R+yOWrvCfYFc24crfZmuHKetY3lgYfhmPmZ3mTSXwlEU/Wo0g0ePn+y0nrafPX/x8tXu3utLZwrLsc+NNPY6BYdSaOyTIInXuUVQqcSrdPq5ql99QeuE0Rc0z3GoYKxFJjiQR+d0s9uJutEyws0kXiUdtoqzm73mcTIyvFCoiUtwbhBHOQ1LsCS4xEU7KRzmwKcwxoFPNSh0w3J500X41pNRmBnrj6ZwSf83SlDOzVXqOxXQxD2sVbCuNigo+zQshc4LQs3vBmWFDMmE1bPDkbDISc59AtwKf9eQT8ACJ/85a1NS5d+g8Ss3SoEelQnYsYLZokyqqSYvE6tCz75XMJFCCXI1htA1hodbDVfkm0YFtxpCZ5tGBesNP93jb7ju/KVbJJjVSff0n6RgiuDXj/yHthPeO4XZKZAVM7+D7ij+cN9haILWb138cMc2k8v33TjqxueHnd7xav9a7IC9Ye9YzD6yHjthZ6zPOEN2y36wn83fQSNoBe271mZj5eyztQj2/wCDnx/G</latexit> <latexit sha1_base64="HW0NkVNdxtG8JSmuoj2JEWTs8bY=">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</latexit> <latexit sha1_base64="0uStd8PEwCtmctIFyVxU/PU2PFc=">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</latexit> [Koyama+ ICASSP 2014] <latexit sha1_base64="TcKdDousfow9G7Auxdzcf+KrT68=">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</latexit>
  20. Sparse optimization using mixed-norm penalty Ø Acoustic signals are generally

    sparse in time-frequency domain Ø Sparse optimization using mixed-norm penalty March 23, 2021 20 <latexit sha1_base64="jt8UZmLAo4CM+kOHoDXBXXv/2js=">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</latexit> <latexit sha1_base64="XMTa05C+9ds+LrBKIVtxIUVcJmU=">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</latexit> <latexit sha1_base64="jNNevYceU70kmgc9X62mIHeNJOc=">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</latexit> <latexit sha1_base64="UO/CtIGxHZlCwhDll94dyV4o5hI=">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</latexit> Optimization algorithm based on Majorization minimization method [Murata+ IEEE TSP 2018] Acoustic signal in time- frequency domain
  21. Super-resolution in recording and reproduction Ø Experimental results using real

    data – Reproduction of speech signal from loudspeaker March 23, 2021 21 Spatial aliasing artifacts originating from microphone intervals can be alleviated Proposed Method based on plane- wave decomposition [Koyama+ JASA 2018]
  22. SOUND FIELD CONTROL March 23, 2021 22

  23. Sound field control using distributed array Ø Synthesize desired sound

    field inside using distributed loudspeakers March 23, 2021 23 <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit> Desired sound field Synthesized sound field Driving signal of th loudspeaker multiplied by transfer function Difficult to directly optimize because integration w.r.t. is included <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit>
  24. Pressure matching Ø Synthesize desired sound field inside using distributed

    loudspeakers March 23, 2021 24 Desired pressure distribution Transfer function matrix Loudspeaker driving signals - Discretize target region and obtain driving signals so that pressure on control points corresponds to desired one <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit> Difficult to densely measure transfer functions inside region <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit>
  25. Pressure matching Ø Synthesize desired sound field inside using distributed

    loudspeakers March 23, 2021 25 - Control points only on boundary of ? <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit> Significant degradation at several frequencies (Forbidden frequency problem) Can be alleviated by placing several control points inside target region, but to determine positions and number of these points is very difficult. <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit>
  26. Weighted mode-matching Ø Control based on spherical wavefunction expansion of

    sound field March 23, 2021 26 [Ueno+ IEEE/ACM TASLP 2019] - Optimization problem including regional integral results in minimization problem w.r.t. expansion coefficients Expansion coeff of desired field Weighting matrix determined by regional integral Expansion coeff of transfer func
  27. Weighted mode-matching Ø Control based on spherical wavefunction expansion of

    sound field March 23, 2021 27 [Ueno+ IEEE/ACM TASLP 2019] ü Truncation of expansion order can be avoided by weighting matrix ü Regional priority of control can be taken into consideration - Optimization problem including regional integral results in minimization problem w.r.t. expansion coefficients
  28. Weighted mode-matching Ø Results of simulation experiment March 23, 2021

    28 -2 0 2 x (m) -2 0 2 y (m) -1 -0.5 0 0.5 1 Amplitude (real part) Synthesis of plane wave Generating quiet zone Suppression of external radiation Also applicable to multizone reproduction and external radiation suppression [Ueno+ IEEE/ACM TASLP 2019]
  29. Optimization of source and sensor placement Ø Optimizing placement of

    loudspeakers and control points in pressure matching March 23, 2021 29 Dense sampling is Inherently necessary
  30. Optimization of source and sensor placement Ø Optimizing placement of

    loudspeakers and control points in pressure matching March 23, 2021 30 Select optimal placement from candidates w.r.t. control accuracy and filter stability
  31. Optimization of source and sensor placement Ø Optimizing placement of

    loudspeakers and control points in pressure matching March 23, 2021 31 - Optimal placement method based on Empirical Interpolation Method [Koyama+ IEEE ICASSP 2018] Sound field control problem is regarded as function interpolation problem: approximate desired sound field by using transfer functions as interpolation functions, control points as sampling points. Applied Empirical Interpolation Method proposed in numerical analysis of PDEs.
  32. Optimization of source and sensor placement Ø Results of simulation

    experiments at 800Hz March 23, 2021 32 -2 0 2 x [m] -2 0 2 4 y [m] -2 0 2 x [m] -2 0 2 4 y [m] -0.5 0 0.5 x [m] -0.5 0 0.5 y [m] -1 0 1 -0.5 0 0.5 x [m] -0.5 0 0.5 y [m] -1 0 1 Proposed Regular Placement Pressure [Koyama+ IEEE ICASSP 2018] -0.5 0 0.5 x [m] -0.5 0 0.5 y [m] -40 -30 -20 -10 0 10 -0.5 0 0.5 x [m] -0.5 0 0.5 y [m] -40 -30 -20 -10 0 10 Error
  33. Conclusion Ø Sound field analysis and control – Analysis: Harmonic

    analysis of infinite orders and its application to spatial ANC, Reconstruction based on sparse decomposition – Control: Weighted mode-matching, Optimization of source and sensor placement for sound field control Ø Recent topics – Kernel learning in sound field interpolation, Interpolation of region-to-region acoustic transfer function, Sensor/source placement optimization, Spatial ANC Ø Keywords – Kernel method, Gaussian process, Reproducing kernel Hilbert space, Sparse modeling, Adaptive filter, Convex optimization, Physical acoustics, Partial differential equation March 23, 2021 33