Towards Sheaf Theoretic Analyses for Delay Tolerant Networking

Short, R.T.; Hylton, Alan; Cardona, Robert; Green, Robert C.; Bainbridge, Gabriel; Moy, Michael; Cleveland, Jacob

doi:10.1109/aero50100.2021.9438167

Cited by 8 publications

(1 citation statement)

References 15 publications

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“…This article uses a diagrammatic approach to topological signal processing, in which measurements of a signal are localized to portions of an arbitrary topological space using the formalism of a sheaf [7]. Due to their expressivity, sheaves have become popular tools for studying sensor and communication problems [8][9][10][11][12]. Our algorithm is an incremental minimization of sheaf local consistency radius, which is a general framework for solving sensing problems [13][14][15].…”

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confidence: 99%

Super-resolving star clusters with sheaves

Robinson

Capraro

2022

EURASIP J. Adv. Signal Process.

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This article presents an optimization-based approach for counting and localizing stars within a small cluster, based on photon counts in a focal plane array. The array need not be arranged in any particular way, and relatively small numbers of photons are required to ensure convergence. The stars can be located close to one another, as the location and magnitude errors were found to be low when the separation was larger than 0.2 Rayleigh radii. To ensure generality of our approach, it was constructed as a special case of a general theory built upon topological signal processing using the mathematics of sheaves that is applicable to general source decomposition problems.

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