  Of interest is the characterization of a cancellous bone immersed in an
acoustic fluid. The bone is placed between an ultrasonic point source and a
receiver. Cancellous bone is regarded as a porous medium saturated with fluid
according to Biot's theory. This model is coupled with the fluid in an open
pore configuration and solved by means of the Finite Volume Method.
Characterization is posed as a Bayesian parameter estimation problem in Biot's
model given pressure data collected at the receiver. As a first step we present
numerical results in 2D for signal recovery. It is shown that as point
estimators, the Conditional Mean outperforms the classical PDE-constrained
minimization solution.

Numerical Analysis