Low-complexity Graph Sampling With Noise and Signal Reconstruction via Neumann Series

Graph sampling addresses the problem of selecting a node subset in a graph to collect samples, so that a K-bandlimited signal can be reconstructed with high fidelity. Assuming an independent and identically distributed (i.i.d.) noise model, minimizing the expected mean square error (MMSE) leads to t...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:IEEE transactions on signal processing Ročník 67; číslo 21; s. 5511 - 5526
Hlavní autoři: Wang, Fen, Cheung, Gene, Wang, Yongchao
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.11.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Approximation
Complexity theory
Covariance matrices
Fourier transforms
Graph signal processing
Inversions
Laplace equations
Matrix decomposition
matrix inversion
Neumann series theorem
Noise
Optimality criteria
Optimization
Robustness (mathematics)
Sampling
Sampling methods
Signal reconstruction
Strategy
ISSN:1053-587X, 1941-0476
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:Graph sampling addresses the problem of selecting a node subset in a graph to collect samples, so that a K-bandlimited signal can be reconstructed with high fidelity. Assuming an independent and identically distributed (i.i.d.) noise model, minimizing the expected mean square error (MMSE) leads to the known A-optimality criterion for graph sampling, which is expensive to compute and difficult to optimize. In this paper, we propose an augmented objective based on Neumann series that well approximates the A-optimal criterion and is amenable to greedy optimization. Specifically, we show that a shifted A-optimal criterion can be equivalently written as a function of an ideal low-pass (LP) graph filter, which in turn can be approximated efficiently via fast graph Fourier transform (FGFT). Minimizing the new objective, we select nodes greedily without large matrix inversions using a matrix inverse lemma. Further, for the dynamic subset sampling case where node availability varies across time, we propose an extended sampling strategy that replaces offline samples one-by-one in the selected set. For signal reconstruction, we propose an accompanied biased signal recovery strategy that reuses the approximated filter from sampling. Experiments show that our reconstruction is more robust to large noise than the least squares (LS) solution, and our sampling strategy far outperforms several existing schemes.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2019.2940129