4 papers · 1 filter
A persistent-homology-Gaussian prior for solving infinite-dimensional Bayesian inverse scattering problems
Zhiyuan Wang, Hang Qi, Xiaofei Guan +2
Bayesian inference methods have been developed to address inverse problems in function spaces where the unknown parameters are of infinite dimension. However, conventional Gaussian…
Fourier--Hankel Moment Recovery in Acoustic Scattering: Multichannel Stabilization and Radial Interface Resolution
Zhiliang Deng, Xiaofei Guan, Xiaomei Yang
We study direct recovery of visible phase centers and concentric radial interfaces from full-aperture acoustic far-field data under the Born approximation. Two complementary moment…
A novel viewpoint for Bayesian inversion based on the Poisson point process
Zhiliang Deng, Zhiyuan Wang, Xiaomei Yang +1
We present a novel Bayesian framework for inverse problems in which the pos terior distribution is interpreted as the intensity measure of a Poisson point process (PPP). The poster…
A persistent-homology-based Bayesian prior for potential coefficient reconstruction in an elliptic PDE
Zhiliang Deng, Haiyang Liu, Xiaofei Guan +2
We address the reconstruction of a potential coefficient in an elliptic partial differential equation from distributed observations within the Bayesian framework. The choice of pri…