  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.
