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Applied Math Seminar - Jameson Cahill

Applied Math Seminar
March 5, 2020
1:45PM - 2:45PM
Math Tower 154

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Add to Calendar 2020-03-05 13:45:00 2020-03-05 14:45:00 Applied Math Seminar - Jameson Cahill Title: Stable group invariant signal representations Speaker: Jameson Cahill - New Mexico State Abstract: In image and audio signal classification, a major problem is to build stable representations that are invariant under rigid motions. Translation invariant representations of signals in C^n are of particular importance. The existence of such representations is intimately related to classical invariant theory, inverse problems in compressed sensing and deep learning. We construct low dimensional representations of signals that are invariant under finite unitary group actions, as a special case we establish the existence of low-dimensional set of measurements which separates the orbits of any cyclic group action, of which translation is one example. Furthermore our map is Lipschitz with respect to the natural metric on the space of orbits. Our construction is closely related to methods use in phase retrieval, so we will give an overview of these methods. Seminar Link Math Tower 154 Department of Mathematics math@osu.edu America/New_York public

Title: Stable group invariant signal representations

Speaker: Jameson Cahill - New Mexico State

Abstract: In image and audio signal classification, a major problem is to build stable representations that are invariant under rigid motions. Translation invariant representations of signals in C^n are of particular importance. The existence of such representations is intimately related to classical invariant theory, inverse problems in compressed sensing and deep learning. We construct low dimensional representations of signals that are invariant under finite unitary group actions, as a special case we establish the existence of low-dimensional set of measurements which separates the orbits of any cyclic group action, of which translation is one example. Furthermore our map is Lipschitz with respect to the natural metric on the space of orbits. Our construction is closely related to methods use in phase retrieval, so we will give an overview of these methods.

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