2024/04/17 by Anuj Abhishek, Abhishek, Anuj, Thilo Strauss +3
Engineering · Medicine · #35J15 #62F15 #62G05 #Advanced X-ray and CT Imaging #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Optical Imaging and Spectroscopy Techniques #Photoacoustic and Ultrasonic Imaging #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2404.11552
openalex publication_date 2024/04/17 · openalex created_date 2024/04/19 · openalex updated_date 2026/07/28
In this article, we propose a non-parametric Bayesian level-set method for simultaneous reconstruction of two different piecewise constant coefficients in an elliptic partial differential equation. We show that the Bayesian formulation of the corresponding inverse problem is well-posed and that the posterior measure as a solution to the inverse problem satisfies a Lipschitz estimate with respect to the measured data in terms of Hellinger distance. We reduce the problem to a shape-reconstruction problem and use level-set priors for the parameters of interest. We demonstrate the efficacy of the proposed method using numerical simulations by performing reconstructions of the original phantom using two reconstruction methods. Posing the inverse problem in a Bayesian paradigm allows us to do statistical inference for the parameters of interest, whereby we are able to quantify the uncertainty in the reconstructions for both methods. This illustrates a key advantage of Bayesian methods over traditional algorithms.