Finite Impulse Response Filters for Simplicial Complexes
Finite Impulse Response Filters for Simplicial Complexes
复制标题
单纯复形的有限脉冲响应滤波器
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
G. Leus
中科院分区：
文献类型：
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作者：
Maosheng Yang;E. Isufi;Michael T. Schaub;G. Leus
在本文中，我们研究了线性滤波器来处理定义在单纯复形上的信号，即，在单纯复形的节点、边、三角形等上定义的信号，从而推广用于图形信号的滤波操作。我们提出了一个有限的脉冲响应滤波器的基础上的霍奇拉普拉斯算子，并演示了如何设计这个滤波器可以放大或衰减某些频谱成分的单纯信号。具体来说，我们讨论如何，不同的情况下，节点信号，傅立叶变换的背景下，边缘信号可以理解的两个正交的子空间对应的梯度流信号和卷曲流信号所产生的霍奇分解。通过将不同的滤波器系数分配给霍奇拉普拉斯算子的相关项，我们开发了一个子空间变化滤波器，可以对这些信号类型进行更细致的控制。数值实验表明单纯滤波器在子分量提取、去噪和模型逼近方面的潜力。
In this paper, we study linear filters to process signals defined on simplicial complexes, i.e., signals defined on nodes, edges, triangles, etc. of a simplicial complex, thereby generalizing filtering operations for graph signals. We propose a finite impulse response filter based on the Hodge Laplacian, and demonstrate how this filter can be designed to amplify or attenuate certain spectral components of simplicial signals. Specifically, we discuss how, unlike in the case of node signals, the Fourier transform in the context of edge signals can be understood in terms of two orthogonal subspaces corresponding to the gradient-flow signals and curl-flow signals arising from the Hodge decomposition. By assigning different filter coefficients to the associated terms of the Hodge Laplacian, we develop a subspace-varying filter which enables more nuanced control over these signal types. Numerical experiments are conducted to show the potential of simplicial filters for sub-component extraction, denoising and model approximation.
DOI：
10.1109/icassp40776.2020.9053655
发表时间：
2020-05
期刊：
ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
影响因子：
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作者：
M. Coutiño;G. V. Karanikolas;G. Leus;G. Giannakis
通讯作者：
M. Coutiño;G. V. Karanikolas;G. Leus;G. Giannakis