信号解析arXiv:2309.04094
多様体上の信号解析におけるガボール枠と高次元境界
Gabor frames and higher dimensional boundaries in signal analysis on manifolds
曲がった多様体上の信号を解析するため、高次元境界を検出できるガボール枠を構成し、ロボットの構成空間への応用を示した。
著者: Vasiliki Liontou, Matilde Marcolli
分類: eess.SP, cs.RO, math.DG, math.FA
原文アブストラクト
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.