MAP estimators for piecewise continuous inversion (Q2832559)

This work discusses the inverse problem of estimating a field from a finite set of nonlinear functionals of the state variable. The focus is on reconstructing piecewise continuous state variable, where the discontinuity is described by a finite number of geometric parameters. The setting covers groundwater flow and electrical impedance tomography. The authors employ a Bayesian formulation with a piecewise continuous fields, and analyze the MAP estimators, which are minimizers of a generalized Onsager-Machlup functional. The theory is illustrated with the groundwater flow, and numerically demonstrated.