Sampling and Recovery of Signals Over Product Cell Structures
ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)(2024)
Abstract
We consider recovery of signals over product cell structures from subsampled observations. In particular, we consider product cell complexes, which can be factorized as the Cartesian product of two simplicial complexes. We focus on recovering edge and node signals from subsampled signals on the factor simplicial complexes. To do so, we first express bandlimited edge signals on the product cell complex as a direct sum of the Kronecker product of bandlimited edge and node signals on the factor simplicial complexes. Then, we propose a simple least squares solution for estimating the edge signal on the product complex. Next, we leverage the Helmholtz-Hodge decomposition on product spaces and propose a simple least squares estimator to recover node signals on the product cell complex. We evaluate the proposed method on both synthetic and real data.
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Key words
Product cell structures,simplicial complexes,simplicial signals
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