Gabor frames and higher dimensional boundaries in signal analysis on manifolds

Vasiliki Liontou; Matilde Marcolli

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arXiv · 2309.04094

Gabor frames and higher dimensional boundaries in signal analysis on manifolds

Vasiliki Liontou·Matilde Marcolli

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Abstract

We provide a construction of Gabor frames that encode local linearizations of a signal detected on a curved smooth manifold of arbitrary dimension, with Gabor filters that can detect the presence of higher-dimensional boundaries in the manifold signal. We describe an application in configuration spaces in robotics with sharp constrains. The construction is a higher-dimensional generalization of the geometric setting developed for the study of signal analysis in the visual cortex.

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Vasiliki Liontou, Matilde Marcolli. 2023-09-08. Gabor frames and higher dimensional boundaries in signal analysis on manifolds. https://arxiv.org/abs/2309.04094

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