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...
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| Vydáno v: | IEEE transactions on signal processing Ročník 67; číslo 21; s. 5511 - 5526 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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IEEE
01.11.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1053-587X, 1941-0476 |
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| Abstract | 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. |
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| AbstractList | Graph sampling addresses the problem of selecting a node subset in a graph to collect samples, so that a [Formula Omitted]-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. 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. |
| Author | Wang, Fen Cheung, Gene Wang, Yongchao |
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| SubjectTerms | 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 |
| Title | Low-complexity Graph Sampling With Noise and Signal Reconstruction via Neumann Series |
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