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ABSTRACT

Newly emerging imaging methods lead to the inverse problem of determining one or several coefficient function(s) in an elliptic partial differential equation from (partial) knowledge of its solutions. A natural and generic approach is to approximate the unknown coefficients by minimizing a linearized and regularized data-fit functional. In this talk, we will show how to regularize the linearized data-fit functional with monotonicity-based constraints in such a way that convergence of certain shape properties in the reconstructions can be rigorously guaranteed.