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Inverse Problems Using Reduced Basis Method, Phil Gralla

All Theses

Inverse Problems is a field of great interest for many applications, such as parameter identification and image reconstruction. The underlying models of inverse problems in many applications often involve Partial Differential Equations (PDEs). A Reduced Basis (RB) method for solving PDE based inverse problems is introduced in this thesis. The RB has been rigorously established as an efficient approach for solving PDEs in recent years. In this work, we investigate whether the RB method can be used as a regularization for solving ill-posed and nonlinear inverse problems using iterative methods. We rigorously analyze the RB method and prove convergence of …