Object based Bayesian full-waveform inversion with topological priors

We propose a full-waveform inversion scheme to detect inhomogeneities in a medium with quatified uncertainty. First, we identify the most prominent anomalous regions by visualizing topological fields associated to functionals comparing the true recorded data with the data that would be obtained from a forward model by varying the geometry of the inhomogeneities and their material parameters. Then, we construct priors based on that information and develop a Bayesian inference framework. We study the posterior distribution over a finite parameter set representing the objects by Markov Chain Monte Carlo sampling and by sampling a Gaussian distribution found by linearization about the maximum a posteriori estimates. We demonstrate the approach on the Bayesian solution of 2D inverse problems in medical elastography and holography