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Bayesian approach for recovering piecewise constant viscoelasticity from MRE data. (English) Zbl 1431.35244

Summary: This paper deals with an inverse problem for recovering the piecewise constant viscoelasticity of a living body from MRE (Magnetic Resonance Elastography) data. Based on a scalar partial differential equation whose solution can approximately simulate MRE data, our inverse coefficient problem is considered as a statistical inverse problem of reconstructing the posterior distribution of unknown viscoelastic modulus. For sampling this distribution, one usually can use the Metropolis-Hastings Markov chain Monte Carlo (MH-MCMC) algorithm. However, without an appropriate “proposal” distribution given artificially, the MH-MCMC algorithm is hard to draw samples efficiently. To avoid this, a so-called slice sampling algorithm is introduced in this paper and applied for solving our problem. The performance of these statistical inversion algorithms is numerically tested basing on simulated data.

MSC:

35R30 Inverse problems for PDEs
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
92C55 Biomedical imaging and signal processing
65C05 Monte Carlo methods
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