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An optimization problem based on a Bayesian approach for the 2D Helmholtz equation. (English) Zbl 1451.35261
Summary: Elastography is a ill-posed inverse problem that aims at recovering the Lamé and density of the domain of interest from finite number of observations, we consider as model the Helmoltz equation. We present an implementation for solving the Helmholtz inverse problem in two dimensions via an optimization problem based on Bayesian approach. In addition, the accuracy of the method is also investigated with respect to the amount of information taken from the generalized Hermitian Eigenvalue problem and by comparing the maximum a posterior estimate to the true parameter distribution in simulated experiments.
35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
Full Text: DOI
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