Nonstationary inversion is a subfield of Bayesian paradigm for inverse problems. The most common formulation is based on the state space representation, or the evolution-observation representation, for the underlying problem. The stochastic convection-diffusion equation is the most common evolution model in industrial problems. This model contains the flow field as a vector-valued distributed parameter, and this parameter is commonly not known exactly.The simultaneous estimation of the state variable (typically conductivity or concentration) and the flow field is an unidentifiable problem with measurement models that correspond to inverse problems. It is possible, however, to estimate a low-dimensional approximation of the flow field simultaneously. We discuss the selection of the representations and the general statistical, numerical and computational aspects of this problem. We strart, however, with a general introduction to process tomography and the related modelling problems.
Seminar on Analysis at University of Tsukuba