Dynamical Programming for off-the-grid dynamic Inverse Problems
Tovey, Robert; Duval, Vincent (2022), Dynamical Programming for off-the-grid dynamic Inverse Problems. https://basepub.dauphine.psl.eu/handle/123456789/23597
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Type
Document de travail / Working paperDate
2022Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSLPublished in
Paris
Pages
43
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Show full item recordAuthor(s)
Tovey, RobertCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Duval, Vincent

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this work we consider algorithms for reconstructing time-varying data into a finite sum of discrete trajectories, alternatively, an off-the-grid sparse-spikes decomposition which is continuous in time. Recent work showed that this decomposition was possible by minimising a convex variational model which combined a quadratic data fidelity with dynamical Optimal Transport. We generalise this framework and propose new numerical methods which leverage efficient classical algorithms for computing shortest paths on directed acyclic graphs. Our theoretical analysis confirms that these methods converge to globally optimal reconstructions which represent a finite number of discrete trajectories. Numerically, we show new examples for unbalanced Optimal Transport penalties, and for balanced examples we are 100 times faster in comparison to the previously known method.Related items
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