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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.
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 i
In this work, we are interested in the determination of the shape of the scatterer for the two dimensional time harmonic inverse medium scattering problems in acoustics. The scatterer is assumed to be a piecewise constant function with a known value
We consider the inverse source problems with multi-frequency sparse near field measurements. In contrast to the existing near field operator based on the integral over the space variable, a multi-frequency near field operator is introduced based on t
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 f
In this paper we consider a level set reinitialization technique based on a high-order, local discontinuous Galerkin method on unstructured triangular meshes. A finite volume based subcell stabilization is used to improve the nonlinear stability of t