1,721,035 research outputs found
A Continuum Mechanical Approach to Geodesics in Shape Space
No full text1 online resource (PDF, 38 pages, includes illustrations)Wirth, Benedikt; Bar, Leah; Rumpf, Martin; Sapiro, Guillermo. (2010). A Continuum Mechanical Approach to Geodesics in Shape Space. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/180741
Dynamic Cell Imaging in PET With Optimal Transport Regularization
No full textWe propose a novel dynamic image reconstruction method from PET listmode data that could be particularly suited to tracking single or small numbers of cells. In contrast to conventional PET reconstruction our method combines the information from all detected events not only to reconstruct the dynamic evolution of the radionuclide distribution, but also to improve the reconstruction at each single time point by enforcing temporal consistency. This is achieved via optimal transport regularization where in principle, among all possible temporally evolving radionuclide distributions consistent with the PET measurement, the one is chosen with least kinetic motion energy. The reconstruction is found by convex optimization so that there is no dependence on the initialization of the method. We study its behaviour on simulated data of a human PET system and demonstrate its robustness even in settings with very low radioactivity. In contrast to previously reported cell tracking algorithms, our technique is oblivious to the number of tracked cells. Without any additional complexity one or multiple cells can be reconstructed, and the model automatically determines the number of particles. For instance, four radiolabelled cells moving at a velocity of 3.1 mm/s and a PET recorded count rate of 1.1 cps (for each cell) could be simultaneously tracked with a tracking accuracy of 5.3 mm inside a simulated human body
Dynamic models of Wasserstein-1-type unbalanced transport
No full textWe consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which transport costs are proportional to transport distance. For those models we derive an equivalent, computationally more efficient static formulation, we perform a detailed analysis of the model optimizers and the associated optimal mass change and transport, and we examine which static models are generated by a corresponding equivalent dynamic one. Alongside we discuss thoroughly how the employed model formulations relate to other formulations found in the literature.</jats:p
Duality in Branched Transport and Urban Planning
No full textAbstract
In recent work (Lohmann et al. in J Math Pures Appl, 2022,
https://doi.org/10.1016/j.matpur.2022.05.021
, Theorem 1.3.4) we have shown the equivalence of the widely used nonconvex (generalized) branched transport problem with a shape optimization problem of a street or railroad network, known as (generalized) urban planning problem. The argument was solely based on an explicit construction and characterization of competitors. In the current article we instead analyse the dual perspective associated with both problems. In more detail, the shape optimization problem involves the Wasserstein distance between two measures with respect to a metric depending on the street network. We show a Kantorovich–Rubinstein formula for Wasserstein distances on such street networks under mild assumptions. Further, we provide a Beckmann formulation for such Wasserstein distances under assumptions which generalize our previous result in [16]. As an application we then give an alternative, duality-based proof of the equivalence of both problems under a growth condition on the transportation cost, which reveals that urban planning and branched transport can both be viewed as two bilinearly coupled convex optimization problems.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Alfried Krupp von Bohlen und Halbach-Stiftung http://dx.doi.org/10.13039/50110000530
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