An optimization problem based on a Bayesian approach for the 2D Helmholtz equation

Abstract

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.

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Correspondence to Lili Guadarrama.

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Guadarrama, L., Prieto, C. & Van Houten, E. An optimization problem based on a Bayesian approach for the 2D Helmholtz equation. Bol. Soc. Mat. Mex. 26, 1097–1111 (2020). https://doi.org/10.1007/s40590-020-00302-2

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Keywords

  • Helmholtz equation
  • Inverse problem
  • Bayesian inference
  • Elastography

Mathematics Subject Classification

  • 35R30
  • 65N21