Wednesday January 14th, 2026 03:00 PM
B700 + Zoom
Speaker:Julius Lohmann JSPS International Research Fellow, Institute of Science Tokyo
Title: Dynamic inverse problems regularized with Wasserstein-1 transport Julius Lohmann JSPS International Research Fellow, Institute of Science Tokyo
Abstract: The (classical, balanced) Wasserstein-p distance can be used as a measure of how close a source and sink mass distribution (with equal mass) are. In recent years, the Wasserstein-2 distance has been employed in the temporal regularization of dynamic inverse problems. The so-called Benamou–Brenier formula states that it can be written as the square root of the performed physical work through the transport from the source to the sink. In my talk, I will instead focus on dynamic inverse problems regularized with Wasserstein-1 transport. The Wasserstein-1 distance can be interpreted as the optimal transport cost with respect to the Euclidean distance: it equals infπ R |x−y|dπ(x, y), where measure element dπ(x, y) indicates the (infinitesimal) amount of mass moving from location x to y. I will explain a novel dynamic inverse problem on time-parameterized curves in the induced Wasserstein-1 (metric) space. It is a natural extension of static sparse optimization problems such as lasso or TV regularization. One essential difference to classical regularization with Wasserstein-2 transport is that it allows for discontinuous decision variables (realized as BV curves). Despite this weak regularity requirement and the non-differentiability of the cost function (x, y) 7→ |x − y|, it is possible to prove the existence of a sparse solution and its characterization. I will present this result. Further, I will detail an adaption of the fully-corrective generalized conditional gradient method to the problem and highlight a natural discretization approach. Finally, I will show some numerical examples. Joint work with: Marcello Carioni
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