An ensemble Kalman filter approach based on level set parameterization for acoustic source identification using multiple frequency information

The spatial dependent unknown acoustic source is reconstructed according noisy multiple frequency data on a remote closed surface. Assume that the unknown function is supported on a bounded domain. To determine the support, we present a statistical inversion algorithm, which combines the ensemble Kalman filter approach with level set technique. Several numerical examples show that the proposed method give good numerical reconstruction.

A parametric Bayesian level set approach for acoustic source identification using multiple frequency information

The reconstruction of the unknown acoustic source is studied using the noisy multiple frequency data on a remote closed surface. Assume that the unknown source is coded in a spatial dependent piecewise constant function, whose support set is the target to be determined. In this setting, the unknown source can be formalized by a level set function. The function is explored with Bayesian level set approach. To reduce the infinite dimensional problem to finite dimension, we parameterize the level set function by the radial basis expansion. The well-posedness of the posterior distribution is proven. The posterior samples are generated according to the Metropolis-Hastings algorithm and the sample mean is used to approximate the unknown. Several shapes are tested to verify the effectiveness of the proposed algorithm. These numerical results show that the proposed algorithm is feasible and competitive with the Matern random field for the acoustic source problem.

Bayesian approach for inverse obstacle scattering with Poisson data

We consider an acoustic obstacle reconstruction problem with Poisson data. Due to the stochastic nature of the data, we tackle this problem in the framework of Bayesian inversion. The unknown obstacle is parameterized in its angular form. The prior for the parameterized unknown plays key role in the Bayes reconstruction algorithm. The most popular used prior is the Gaussian. Under the Gaussian prior assumption, we further suppose that the unknown satisfies the total variation prior. With the hybrid prior, the well-posedness of the posterior distribution is discussed. The numerical examples verify the effectiveness of the proposed algorithm.