Sparse Regularization Techniques for Efficient Inverse Problem Solving with Application in Contaminant Dispersion
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Inverse problems are typically ill-posed and therefore cannot be solved reliably without additional assumptions. Regularization methods are commonly employed to restore well-posedness and to incorporate prior information into the reconstruction. In this talk, we demonstrate how sparsity-promoting regularization can be used to address inverse problems arising in the protection of critical infrastructures, e.g., sparse source identification in contaminant dispersion scenarios. Using a Primal-Dual-Active-Point strategy, the infinite-dimensional optimization problem can be reduced to a sequence of finite-dimensional subproblems involving an ℓ1-regularization term. These subproblems are efficiently solved with a semismooth Newton method. Numerical results illustrate the effectiveness of the proposed approach in identifying sparse parameters, and, finally, we outline how the implemented algorithm can help to improve situational awareness and mitigate impact of gas leakage incidents.
