Object based Bayesian full-waveform inversion for shear elastography
Ana Carpio Elena Cebrian Andrea Gutierrez
We develop a computational framework to quantify uncertainty in shear
elastography imaging of anomalies in tissues. We adopt a Bayesian inference
formulation. Given the observed data, a forward model and their uncertainties,
we find the posterior probability of parameter fields representing the geometry
of the anomalies and their shear moduli. To construct a prior probability, we
exploit the topological energies of associated objective functions. We
demonstrate the approach on synthetic two dimensional tests with smooth and
irregular shapes. Sampling the posterior distribution by Markov Chain Monte
Carlo (MCMC) techniques we obtain statistical information on the shear moduli
and the geometrical properties of the anomalies. General affine-invariant
ensemble MCMC samplers are adequate for shapes characterized by parameter sets
of low to moderate dimension. However, MCMC methods are computationally
expensive. For simple shapes, we devise a fast optimization scheme to calculate
the maximum a posteriori (MAP) estimate representing the most likely parameter
values. Then, we approximate the posterior distribution by a Gaussian
distribution found by linearization about the MAP point to capture the main
mode at a low computational cost.