Uncertainty Characterization in Model-Based Inverse and Imaging Problems

Monday, April 29, 2019 - 11:20am - 12:10pm
Lind 305
Kui Ren (Columbia University)
In model-based inverse and imaging problems, it is often the case that only a portion of the relevant physical quantities in the model can be reconstructed/imaged. The rest of the model parameters are assumed to be known. In practice, these parameters are often only known partially (up to a certain accuracy). It is therefore important to characterize the dependence of the inversion/imaging results on the accuracy of these parameters. This is an uncertainty quantification problem that is challenging due to the fact that both the map from the uncertainty parameters (the ones we assumed partially known) to the measured data and the map from the measured data to the quantities to be imaged are difficult to analyze. In this talk, we review some recent computational and mathematical results on such uncertainty characterization problems in nonlinear inverse problems for PDEs. This talk is based on joint work with Yimin Zhong and Sarah Vallelian