Sparse Representation of a Spatial Sound Field in a Reverberant Environment

This paper investigates sound-field modeling in a realistic reverberant setting. Starting from a few point-like microphone measurements, the goal is to estimate the direct source field within a whole three-dimensional (3-D) space around these microphones. Previous sparse sound field decompositions assumed only a spatial sparsity of the source distribution, but could generally not handle reverberation. We here add an explicit model of the reverberant sound field, that has two components: the first component sparse in the plane-wave domain, the other component low-rank as a multiplication of transfer functions and source signals. We derive the corresponding decomposition algorithm based on the alternating direction method of multipliers. We furthermore provide empirical rules for tuning the two parameters to be set in the algorithm. Numerical and experimental results indicate that the decomposition and reconstruction performances are significantly improved, in the case of reverberant environments.

[1]  J. D. Maynard,et al.  Nearfield acoustic holography: I. Theory of generalized holography and the development of NAH , 1985 .

[2]  Hiroshi Saruwatari,et al.  Sound Field Recording Using Distributed Microphones Based on Harmonic Analysis of Infinite Order , 2018, IEEE Signal Processing Letters.

[3]  Shoichi Koyama,et al.  Sparse sound field representation in recording and reproduction for reducing spatial aliasing artifacts , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[4]  Y. Nesterov.  A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .

[5]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[6]  Shoichi Koyama,et al.  Comparison of reverberation models for sparse sound field decomposition , 2017, 2017 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA).

[7]  B. Rafaely,et al.  Sound-field analysis by plane-wave decomposition using spherical microphone array , 2005 .

[8]  Bhaskar D. Rao,et al.  Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm , 1997, IEEE Trans. Signal Process..

[9]  Hiroshi Saruwatari,et al.  Sparse Representation Using Multidimensional Mixed-Norm Penalty With Application to Sound Field Decomposition , 2018, IEEE Transactions on Signal Processing.

[10]  Michael Elad,et al.  Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing , 2010 .

[11]  Pablo A. Parrilo,et al.  Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization , 2007, SIAM Rev..

[12]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[13]  Holography Book,et al.  Fourier Acoustics Sound Radiation And Nearfield Acoustical Holography , 2016 .

[14]  Zhixun Su,et al.  Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation , 2011, NIPS.

[15]  Hiroshi Saruwatari,et al.  Sparse sound field decomposition for super-resolution in recording and reproduction. , 2018, The Journal of the Acoustical Society of America.

[16]  Bhaskar D. Rao,et al.  Sparse solutions to linear inverse problems with multiple measurement vectors , 2005, IEEE Transactions on Signal Processing.

[17]  Mark A. Poletti,et al.  Three-Dimensional Surround Sound Systems Based on Spherical Harmonics , 2005 .

[18]  Walter Kellermann,et al.  Acoustic source detection and localization based on wavefield decomposition using circular microphone arrays , 2006 .

[19]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[20]  Patrick L. Combettes,et al.  Signal Recovery by Proximal Forward-Backward Splitting , 2005, Multiscale Model. Simul..

[21]  Sean F. Wu,et al.  Helmholtz equation-least-squares method for reconstructing the acoustic pressure field , 1997 .

[22]  Craig T. Jin,et al.  Upscaling Ambisonic sound scenes using compressed sensing techniques , 2011, 2011 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA).

[23]  Efren Fernandez-Grande,et al.  Sound field reconstruction using a spherical microphone array. , 2016, The Journal of the Acoustical Society of America.

[24]  Julian D. Maynard,et al.  Sound source reconstructions using a microphone array , 1980 .

[25]  J. B. Fahnline,et al.  A method for computing acoustic fields based on the principle of wave superposition , 1989 .

[26]  Frédéric Hecht,et al.  New development in freefem++ , 2012, J. Num. Math..

[27]  Laurent Daudet,et al.  Room Reverberation Reconstruction: Interpolation of the Early Part Using Compressed Sensing , 2013, IEEE Transactions on Audio, Speech, and Language Processing.

[28]  S. Elliott,et al.  AN EQUIVALENT SOURCE TECHNIQUE FOR CALCULATING THE SOUND FIELD INSIDE AN ENCLOSURE CONTAINING SCATTERING OBJECTS , 1998 .

[29]  Prasanga N. Samarasinghe,et al.  Wavefield Analysis Over Large Areas Using Distributed Higher Order Microphones , 2014, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

[30]  Hiroshi Saruwatari,et al.  Sound field decomposition in reverberant environment using sparse and low-rank signal models , 2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[31]  Rémi Gribonval,et al.  Near-field acoustic holography using sparse regularization and compressive sampling principles. , 2012, The Journal of the Acoustical Society of America.

[32]  Shoichi Koyama,et al.  Analytical Approach to Wave Field Reconstruction Filtering in Spatio-Temporal Frequency Domain , 2013, IEEE Transactions on Audio, Speech, and Language Processing.

[33]  Ralf Hiptmair,et al.  Plane wave approximation of homogeneous Helmholtz solutions , 2011 .

[34]  Volkan Cevher,et al.  Model-based sparse component analysis for reverberant speech localization , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[35]  P. Nelson,et al.  ESTIMATION OF ACOUSTIC SOURCE STRENGTH BY INVERSE METHODS: PART I, CONDITIONING OF THE INVERSE PROBLEM , 2000 .