A classical inverse problem arising in seismological and ultrasound imaging is the identification from wave-field data of those spatially varying parameters which determine the propagation of the acoustic wave field. This is often called the inverses scattering problem or the diffraction tomography problem. We define a physically based likelihood for 2D acoustic imaging of an inhomogeneous, isotropic acoustic medium. We then turn to the problem of decomposing this likelihood into a form that is amenable to efficient Markov chain Monte Carlo simulation. In particular, we give an approximation to the likelihood allowing those localized MCMC updates which are rejected to the computed with worst case time complexity of order constant.
Geoff K. Nicholls,
"Physically based likelihood for ultrasound imaging", Proc. SPIE 3459, Bayesian Inference for Inverse Problems, (22 September 1998); doi: 10.1117/12.323788; https://doi.org/10.1117/12.323788