Sampling in the Euclidean Motion Group and a Problem from Brain's Primary Visual Cortex

We study a sampling problem for the abstract wavelet transform associated with the quasiregular representation of the $SE(2)$ group, for a modulated gaussian mother wavelet. This problem is motivated by the behavior of brain's primary visual cortex. We provide a characterization in terms of a dual Gramian matrix, and study numerically the relationships among the parameters defining the sampling and the mother wavelet.

Source: arXiv:2601.17528v1 - http://arxiv.org/abs/2601.17528v1 PDF: https://arxiv.org/pdf/2601.17528v1 Original Link: http://arxiv.org/abs/2601.17528v1