Finite Impulse Response Filters for Simplicial Complexes

European Signal Processing Conference (EUSIPCO), pp. 2005–2009

Abstract

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.

Authors 4

1. Maosheng Yang

   Delft University of Technology

   Affiliation as printed

   Dept. of Intelligent Systems, Delft University of Technology, Delft, The Netherlands

   (Delft University of Technology)

2. Elvin Isufi

   Delft University of Technology

   Affiliation as printed

   Dept. of Intelligent Systems, Delft University of Technology, Delft, The Netherlands

   (Delft University of Technology)

3. Michael T. Schaub Aachen Department of Computer Science

   RWTH Aachen University

   Affiliation as printed

   Dept. of Computer Science, RWTH Aachen University, Aachen, Germany

   RWTH Aachen University

4. Geert J. T. Leus

   Delft University of Technology

   Affiliation as printed

   Dept. of Microelectronics, Delft University of Technology, Delft, The Netherlands

   (Delft University of Technology)