Generalized signals on simplicial complexes
Signal Processing
2023-11-14 v2 Information Theory
math.IT
Abstract
Topological signal processing (TSP) over simplicial complexes typically assumes observations associated with the simplicial complexes are real scalars. In this paper, we develop TSP theories for the case where observations belong to general abelian groups, including function spaces that are commonly used to represent time-varying signals. Our approach generalizes the Hodge decomposition and allows for signal processing tasks to be performed on these more complex observations. We propose a unified and flexible framework for TSP that expands its applicability to a wider range of signal processing applications. Numerical results demonstrate the effectiveness of this approach and provide a foundation for future research in this area.
Keywords
Cite
@article{arxiv.2305.06899,
title = {Generalized signals on simplicial complexes},
author = {Feng Ji and Xingchao Jian and Wee Peng Tay and Maosheng Yang},
journal= {arXiv preprint arXiv:2305.06899},
year = {2023}
}