Title: Enhancing resolution in inverse problems based on a reduced model (Part 1)
Speaker: Erkki Somersalo (Professor and Interim Chair, Case Western Reserve University)
Abstract: When solving inverse problems under demanding conditions, e.g., when the computational time is an issue, an attractive option is to replace a costly high-fidelity forward model by a reduced model that requires less computing resources. When doing so, an unpredictable modeling error is introduced, and since inverse problems are ill-conditioned by nature, this error propagates to the computed solution of the problem, often rendering the solution useless.
In this series of lectures, we consider a model problem, the electrical impedance tomography (EIT) problem, and discuss the effect of the modeling error arising from low accuracy finite element discretization of the underlying elliptic PDE. The first talk gives the computational background of the forward problem, and in the sequel, the inverse problem is discussed in a statistical framework, in which the modeling error can be properly addressed. Computed numerical examples demonstrate how dramatic the effect of proper description of the modeling error is in practice. Extensions of the approach to other computational problems are also discussed.