Signal Processing On Cell Complexes

IEEE International Conference on Acoustics Speech and Signal Processing, pp. 8852–8856

Abstract

The processing of signals supported on non-Euclidean domains has attracted large interest recently. Thus far, such non-Euclidean domains have been abstracted primarily as graphs with signals supported on the nodes, though the processing of signals on more general structures such as simplicial complexes has also been considered. In this paper, we give an introduction to signal processing on (abstract) regular cell complexes, which provide a unifying framework encompassing graphs, simplicial complexes, cubical complexes and various meshes as special cases. We discuss how appropriate Hodge Laplacians for these cell complexes can be derived. These Hodge Laplacians enable the construction of convolutional filters, which can be employed in linear filtering and non-linear filtering via neural networks defined on cell complexes.

Authors 3

1. T. Mitchell Roddenberry

   Rice University

   Affiliation as printed

   Rice University,Department of Electrical and Computer Engineering,USA

   Department of Electrical and Computer Engineering, Rice University, USA

2. Michael T. Schaub Aachen Department of Computer Science

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Department of Computer Science,Germany

   Department of Computer Science, RWTH Aachen University, Germany

3. Mustafa Hajij

   Santa Clara University

   Affiliation as printed

   Santa Clara University,Department of Mathematics and Computer Science,USA

   Department of Mathematics and Computer Science, Santa Clara University, USA