Sound field decomposition enables to estimate and interpolate an acoustic field inside a region including sources. Such a decomposition generally requires the discretization of a region of interest into a set of grid points to apply sparse representation algorithms. On the other hand, a gridless sound field decomposition method based on the reciprocity gap functional makes it possible to decompose it into point sources in a gridless manner with measurements on the boundary surface of the spherical target region. The closed-form algorithm is derived based on the reciprocity gap functional in the spherical harmonic domain with interpolating a sound field on the boundary. In this paper, further investigation on the interpolation methods for the gridless sound field decomposition is performed. The experimental results indicated that the highest accuracy is achieved by our proposed method, especially at high frequencies.
This paper proposes a method for the localization of correlated sources, through the estimation of the covariance matrix of the sources. In order to deal with the ill-posedness of the estimation and take into account the prior informations on the sources (small number of punctual, possibly correlated, sources), the inversion is based on the sparsity and the low-rankedness of the covariance matrix of the sources. Results show that the performances are greatly improved due to the joint use of sparsity and low rank compared to Tikhonov regularization or the use of only one of these priors. Additionaly, the low rank and sparsity constraints improve the resolution of the localization: the ability to separate close sources is improved when each of the source is correlated with another, sufficiently resolved, source. The estimated matrix is obtained through the minimization of a criterion, sum of an error term with respect to the data, the l_1 norm of the coefficients of the matrix to take in to account its sparsity, and the nuclear norm of the covariance matrix, to penalize matrix with high ranks. This numerical optimization problem is solved by SDMM (Simultaneous Direction Method of Multipliers). Moreover, fast SVD of the low-rank matrices can be used to deal with the high-dimensionality of the problem. The performances are illustrated by numerical results obtained with various scenario of correlated sources.
Azimuthal duct mode detection in experiments are particularly beneficial for designing ad-vanced fans and evaluating passive/active noise reduction methods. In this paper, we propose a new mode detection method based on compressed sensing, which can largely reduce the sensor numbers required by Shannon-Nyquist sampling theorem. The success of the com-pressed sensing methodology is based on the fact that incident waves are sparse in spinning modes and the sensors are located randomly. However, when the sensor number is small, the mode detection maybe not successful for many sensor displays. Therefore, besides introduc-ing a more straightforward way of applying compressed sensing method to duct mode detec-tion, this paper also studies properties of the sensor location in order to obtain the expected good mode detection results in the real experiment. The studies of sensor location properties are based on both Monte Carlo simulations and a real experiment test. This makes it quite promising to apply much less sensors in a real experiment and detect mode successfully with compressed sensing algorithm.
This work treats the theory of compressive sensing (CS) for the identification of sound source with attention on the sensor arrangement in the random array. As a lower Restricted Isometry Constant (RIC) is anticipated for satisfying the Restricted Isometry Property (RIP) that assures a stable recovery with CS, an objective function is established with the RIC averaging over the array's intended frequency range. Monte-Carlo based statistical method enables an estimation of RIC in the course of the minimization process, thereby proper sensor positions could be determined. The demonstration examines an optimal arrangement of 24 sensors for a given aperture, which is compared to two different types of random arrays. It is shown that the sen-sor configuration obtained by the proposed approach offers an improved performance as the frequency decreases and/or signal-to-noise ratio gets worse.
