Nearfield Acoustic Holography using sparsity and compressive sampling principles

Regularization of the inverse problem is a complex issue when using Near-field Acoustic Holography (NAH) techniques to identify the vibrating sources. This paper shows that, for convex homogeneous plates with arbitrary boundary conditions, new regularization schemes can be developed, based on the sparsity of the normal velocity of the plate in a well-designed basis, i.e. the possibility to approximate it as a weighted sum of few elementary basis functions. In particular, these new techniques can handle discontinuities of the velocity field at the boundaries, which can be problematic with standard techniques. This comes at the cost of a higher computational complexity to solve the associated optimization problem, though it remains easily tractable with out-of-the-box software. Furthermore, this sparsity framework allows us to take advantage of the concept of Compressive Sampling: under some conditions on the sampling process (here, the design of a random array, which can be numerically and experimentally validated), it is possible to reconstruct the sparse signals with significantly less measurements (i.e., microphones) than classically required. After introducing the different concepts, this paper presents numerical and experimental results of NAH with two plate geometries, and compares the advantages and limitations of these sparsity-based techniques over standard Tikhonov regularization.Comment: Journal of the Acoustical Society of America (2012

Imagerie acoustique par approximations parcimonieuses des sources

In this work the principle of sparsity-based techniques have been applied to acoustic imaging issues. It includes nearfield acoustic holography (NAH), complex sources localization and directivity pattern identification. These techniques consist in the inversion of ill-posed problems which involve the use of regularization schemes. Moreover, standard regularization methods often require a huge number of microphones in order to oversample the acoustic field and therefore avoiding aliasing effects. To overcome these problems, we investigate sparse regularization principles and/or compressive sampling (CS) for the analysis of acoustic fields. CS states that, under the sparsity assumption of the source to recover, it is possible to significantly reduce the number of measurements (i.e., microphones), even well below spatial Nyquist rates. It is shown that sparsity-based NAH techniques lead to significant improvements over standard NAH techniques. A sub-Nyquist random sampling combined with sparse regularization allows the precise source reconstruction. The problem of source localization can be recast in a sparse framework. It acts as a high-resolution localisation method for correlated and uncorrelated sources that lie in the near field or in the far field. The use of sparsity-promoting algorithms allows the localization of complex sources by improving the sparse model with a spherical harmonic dictionary. This method is applied to the identification of sources directivity pattern. Finally, microphone position self-calibration methods are investigated to experimentally manage large microphone arrays.La description parcimonieuse des sources permet une approche nouvelle de l'analyse des champs acoustiques. Durant ce projet, nous avons appliqué ce principe à plusieurs scénarios classiques : l'holographie acoustique de champ proche, la localisation de sources simples ou complexes et l'identification de directivité de sources. Ces méthodes d'imagerie exigent la résolution de problèmes inverses, souvent mal posés, qui nécessitent l'utilisation conjointe de techniques de régularisation. De plus, pour capter l'information utile et assurer de bonnes performances de reconstruction, les techniques traditionnelles d'antennerie nécessitent le déploiement d'un grand nombre de microphones. Dans ces travaux, nous avons envisagé une approche originale de l'analyse des champs acoustiques basée sur l'approximation parcimonieuse des sources, ce qui agit comme un principe de régularisation. Cette formulation permet en outre de tirer profit de la méthode de "compressive sampling" (CS), qui permet de restreindre le nombre de mesures utiles à la résolution du problème inverse si la source à reconstruire admet une représentation suffisamment parcimonieuse. On montre que l'application du CS à l'holographie en champ proche de plaques homogènes et isotropes permet non seulement de mieux régulariser le problème par rapport aux techniques génériques classiques, mais également de diminuer fortement le nombre de microphones en sous-échantillonnant l'hologramme au-delà de la limite imposée par la théorie de Shannon. Le problème de localisation de sources, envisagée comme un problème parcimonieux, permet la localisation avec une haute résolution de sources corrélés, en champ proche comme en champ lointain. Les méthodes de reconstruction parcimonieuse permettent de structurer la base de parcimonie en l'enrichissant avec un modèle de décomposition des sources en harmoniques sphériques pour localiser et identifier la directivité de sources complexes. Ces études ont finalement nécessité le développement de techniques rapides de calibration en position et en gain d'antennes composées d'un grand nombre de microphones

Imagerie acoustique par approximations parcimonieuses des sources

La description parcimonieuse des sources permet une approche nouvelle de l'analyse des champs acoustiques. Dans ce projet, nous avons appliqué ce principe à plusieurs scénarios: l'holographie acoustique de champ proche (NAH), la localisation et l'identification de directivité de sources. Ces méthodes d'imagerie exigent la résolution de problèmes inverses, souvent mal posés, qui nécessitent d'être régularisés. De plus, pour capter l'information utile et assurer de bonnes performances de reconstruction, les techniques traditionnelles d'antennerie imposent le déploiement d'un grand nombre de microphones. Dans ces travaux, nous utilisons l'approximation parcimonieuse des sources comme moyen de régularisation de problèmes d'imagerie. Cette méthode permet en outre de tirer profit du "compressive sampling" (CS), qui permet de diminuer le nombre de mesures utiles à la reconstruction des sources. On montre que l'application du CS à la NAH permet non seulement de mieux régulariser le problème par rapport aux techniques classiques, mais également de diminuer fortement le nombre de microphones en sous-échantillonnant l'hologramme au-delà de la limite imposée par la théorie de Shannon. Le problème de localisation parcimonieuse de sources permet la localisation avec une haute résolution de sources corrélées, en champ proche comme en champ lointain. Nous structurons la base de parcimonie en l'enrichissant avec un modèle de décomposition des sources en harmoniques sphériques pour localiser et identifier la directivité de sources complexes. Ces études ont nécessité le développement de techniques rapides de calibration de grands réseaux de microphonesIn this work the principle of sparsity-based techniques have been applied to acoustic imaging issues. It includes nearfield acoustic holography (NAH), complex sources localization and directivity pattern identification. These techniques consist in the inversion of ill-posed problems which involve the use of regularization schemes. Moreover, standard regularization methods often require a huge number of microphones in order to oversample the acoustic field and therefore avoiding aliasing effects. To overcome these problems, we investigate sparse regularization principles and/or compressive sampling (CS) for the analysis of acoustic fields. CS states that, under the sparsity assumption of the source to recover, it is possible to significantly reduce the number of measurements (i.e., microphones), even well below spatial Nyquist rates. It is shown that sparsity-based NAH techniques lead to significant improvements over standard NAH techniques. A sub-Nyquist random sampling combined with sparse regularization allows the precise source reconstruction. The problem of source localization can be recast in a sparse framework. It acts as a high-resolution localisation method for correlated and uncorrelated sources that lie in the near field or in the far field. The use of sparsity-promoting algorithms allows the localization of complex sources by improving the sparse model with a spherical harmonic dictionary. This method is applied to the identification of sources directivity pattern. Finally, microphone position self-calibration methods are investigated to experimentally manage large microphone arraysPARIS-BIUSJ-Biologie recherche (751052107) / SudocSudocFranceF

Acoustic sources joint localization and characterization using compressed sensing

International audienceIn this work, a Compressed Sensing (CS) strategy is developed in order to jointly achieve two complementary tasks regarding sound sources: localization and identification. Here, the sources are assumed sparse in the spatial domain, and greedy techniques are used for their localization. The case of coherent sources located in a plane is studied both numerically and experimentally at different frequencies. Results show that, in this framework, CS source localization is reliable using a significantly smaller number of microphones than classical techniques (standard or high resolution beamforming techniques), while overcoming some of their pitfalls. We then use a similar technique for the identification of the source nature, i.e. its radiation pattern, and here the sparsity domain is extended to a basis of elementary radiating functions. We present simulation and experimental results using calibrated sources and measurements performed with a 3D array of 80 randomly distributed microphones. This study investigates the limitations of Compressed Sensing in terms of resolution and reliability of the identification, with respect to the number of sensors, the signal to noise ratio and the density of the reconstruction region

NACHOS (Nearfield ACoustic HOlography with Sparse regularization)

Matlab source code & data to reproduce results on Compressive Nearfield Acoustic Holography from the paper Gilles Chardon, Laurent Daudet, Antoine Peillot, François Ollivier, Nancy Bertin, Rémi Gribonval. Nearfield Acoustic Holography using sparsity and compressive sampling principles. Journal of the Acoustical Society of America, acoustical society of america, 2012

NACHOS (Nearfield ACoustic HOlography with Sparse regularization)

Matlab source code & data to reproduce results on Compressive Nearfield Acoustic Holography from the paper Gilles Chardon, Laurent Daudet, Antoine Peillot, François Ollivier, Nancy Bertin, Rémi Gribonval. Nearfield Acoustic Holography using sparsity and compressive sampling principles. Journal of the Acoustical Society of America, acoustical society of america, 2012