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New Results
Bilateral Contracts and Grants with Industry
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New Results
Bilateral Contracts and Grants with Industry
Bibliography


Section: New Results

Group synchronization on grids

Group synchronization requires to estimate unknown elements (θv)vV of a compact group 𝔾 associated to the vertices of a graph G=(V,E), using noisy observations of the group differences associated to the edges. This model is relevant to a variety of applications ranging from structure from motion in computer vision to graph localization and positioning, to certain families of community detection problems.

We focus on the case in which the graph G is the d-dimensional grid. Since the unknowns θv are only determined up to a global action of the group, we consider the following weak recovery question. Can we determine the group difference θu-1θv between far apart vertices u,v better than by random guessing? We prove that weak recovery is possible (provided the noise is small enough) for d3 and, for certain finite groups, for d2. Vice-versa, for some continuous groups, we prove that weak recovery is impossible for d=2. Finally, for strong enough noise, weak recovery is always impossible.