Paper ID: 2309.04094

Gabor frames and higher dimensional boundaries in signal analysis on manifolds

Vasiliki Liontou, Matilde Marcolli

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.

Submitted: Sep 8, 2023