Signal Processing On Product Spaces
IEEE International Conference on Acoustics Speech and Signal Processing, pp. 1–5
Abstract
We establish a framework for signal processing on product spaces of simplicial and cellular complexes. For simplicity, we focus on the product of two complexes representing time and space, although our results generalize naturally to products of simplicial complexes of arbitrary dimension. Our framework leverages the structure of the eigenmodes of the Hodge Laplacian of the product space to jointly filter along time and space. To this end, we provide a decomposition theorem of the Hodge Laplacian of the product space, which highlights how the product structure induces a decomposition of each eigenmode into a spatial and temporal component. Finally, we apply our method to real world data, specifically for interpolating trajectories of buoys in the ocean from a limited set of observed trajectories.
Authors 5
-
Affiliation as printed
Rice University,Department of Electrical and Computer Engineering,USA
Department of Electrical and Computer Engineering, Rice University, USA
-
Affiliation as printed
RWTH Aachen University,Department of Computer Science,Germany
Department of Computer Science, RWTH Aachen University, Germany
-
Affiliation as printed
RWTH Aachen University,Department of Computer Science,Germany
Department of Computer Science, RWTH Aachen University, Germany
-
Affiliation as printed
RWTH Aachen University,Department of Computer Science,Germany
Department of Computer Science, RWTH Aachen University, Germany
-
Affiliation as printed
Rice University,Department of Electrical and Computer Engineering,USA
Department of Electrical and Computer Engineering, Rice University, USA
Cited by 6 stored of 6
6 results
No patents citing this paper on Lens.org (checked 2026-10-06).