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.
Acoustic sources imaging in the sparsity framework