Accepted Paper

Inserted: 19 may 2025
Last Updated: 6 jan 2026

Journal: Inverse Problems
Year: 2025

Abstract:

We investigate a dynamic inverse problem using a regularization which implements the so-called Wasserstein- distance. It naturally extends well-known static problems such as lasso or total variation regularized problems to a (temporally) dynamic setting. Further, the decision variables, realized as BV curves, are allowed to exhibit discontinuities, in contrast to the design variables in classical optimal transport based regularization techniques. We prove the existence and a characterization of a sparse solution. Further, we use an adaption of the fully-corrective generalized conditional gradient method to experimentally justify that the determination of BV curves in the Wasserstein- space is numerically implementable.

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