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Yongchao Wang - One of the best experts on this subject based on the ideXlab platform.

  • Low-complexity Graph Sampling With Noise and Signal Reconstruction via Neumann Series
    IEEE Transactions on Signal Processing, 2019
    Co-Authors: Fen Wang, Gene Cheung, Yongchao Wang
    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.

  • fast sampling of graph signals with noise via Neumann Series conversion
    International Conference on Acoustics Speech and Signal Processing, 2019
    Co-Authors: Fen Wang, Gene Cheung, Yongchao Wang
    Abstract:

    Graph sampling with independent noise towards minimum mean square error (MMSE) leads to the known A-optimality criterion, which is computation-intensive to evaluate and NP-hard to optimize. In this paper, we propose a new low-complexity sampling strategy based on Neumann Series that circumvents large matrix inversion and eigen-decomposition. We first prove that a DC-shifted A-optimality criterion is equivalent to an objective computed using the inverse of a sub-matrix of an ideal graph low-pass (LP) filter. The LP filter matrix can be approximated efficiently via fast Graph Fourier Transform (FGFT). Using the shifted A-optimality objective as a proxy, we then propose a fast algorithm to greedily select samples one-by-one based on a matrix inversion lemma with simple matrix updates. We show that the obtained solution has a performance upper bound via super-modularity analysis. Simulation results show that our proposed sampling strategy has lower complexity and outperforms several existing deterministic sampling schemes.

  • ICASSP - Fast Sampling of Graph Signals with Noise via Neumann Series Conversion
    ICASSP 2019 - 2019 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2019
    Co-Authors: Fen Wang, Gene Cheung, Yongchao Wang
    Abstract:

    Graph sampling with independent noise towards minimum mean square error (MMSE) leads to the known A-optimality criterion, which is computation-intensive to evaluate and NP-hard to optimize. In this paper, we propose a new low-complexity sampling strategy based on Neumann Series that circumvents large matrix inversion and eigen-decomposition. We first prove that a DC-shifted A-optimality criterion is equivalent to an objective computed using the inverse of a sub-matrix of an ideal graph low-pass (LP) filter. The LP filter matrix can be approximated efficiently via fast Graph Fourier Transform (FGFT). Using the shifted A-optimality objective as a proxy, we then propose a fast algorithm to greedily select samples one-by-one based on a matrix inversion lemma with simple matrix updates. We show that the obtained solution has a performance upper bound via super-modularity analysis. Simulation results show that our proposed sampling strategy has lower complexity and outperforms several existing deterministic sampling schemes.

Mohamed Farahat - One of the best experts on this subject based on the ideXlab platform.

Refaat Salem - One of the best experts on this subject based on the ideXlab platform.

  • Mal’cev-Neumann Series over rings satisfy the weak Beachy–Blair condition
    Rendiconti del Circolo Matematico di Palermo (1952 -), 2016
    Co-Authors: Refaat Salem, Mohamed Farahat, Hanan Abd-elmalk
    Abstract:

    In this paper we extend the notion of Beachy-Blair condition to the weak Beachy-Blair condition, then we study the transfer of the weak Beachy-Blair condition between the base ring R and the ring of Mal’cev-Neumann Series \( R((G;\sigma ;\tau ))\).

  • mal cev Neumann Series over rings satisfy the weak beachy blair condition
    Rendiconti Del Circolo Matematico Di Palermo, 2016
    Co-Authors: Refaat Salem, Mohamed Farahat, Hanan Abdelmalk
    Abstract:

    In this paper we extend the notion of Beachy-Blair condition to the weak Beachy-Blair condition, then we study the transfer of the weak Beachy-Blair condition between the base ring R and the ring of Mal’cev-Neumann Series \( R((G;\sigma ;\tau ))\).

  • Zip Property on Malcev-Neumann Series Modules
    Le Matematiche, 2015
    Co-Authors: Hanan Abd-elmalk, Refaat Salem, Abdelaziz E. Radwan
    Abstract:

    Let R be a ring, MR a right R-module, G a totally ordered group, σ a map from G into the group of automorphisms of R which assigns to each x ∈ G an automorphism σ_x ∈ Aut(R), τ a map from G × G to U(R) (the group of unit elements of R) and M((G; σ ; τ)) the Malcev-Neumann Series module. Then, under some certain conditions, we show that MR is a right zip R-module if and only if M((G; σ ; τ))_{R((G;σ ;τ))} is a right zip R((G; σ ; τ))-module, where R((G; σ ; τ)) is the Malcev-Neumann Series ring.

  • MAL'CEV–Neumann Series OVER ZIP AND WEAK ZIP RINGS
    Asian-european Journal of Mathematics, 2012
    Co-Authors: Refaat Salem, A. M. Hassanein, Mohamed Farahat
    Abstract:

    In this paper we show that: if G is a totally ordered group and R is a G-Armendariz ring (an NI ring with nil(R) is nilpotent), then the ring Λ = R((G; σ; τ)) of Mal'cev–Neumann Series is a right zip (weak zip) ring if and only if R is.

  • mal cev Neumann Series over zip and weak zip rings
    Asian-european Journal of Mathematics, 2012
    Co-Authors: Refaat Salem, A. M. Hassanein, Mohamed Farahat
    Abstract:

    In this paper we show that: if G is a totally ordered group and R is a G-Armendariz ring (an NI ring with nil(R) is nilpotent), then the ring Λ = R((G; σ; τ)) of Mal'cev–Neumann Series is a right zip (weak zip) ring if and only if R is.

Fen Wang - One of the best experts on this subject based on the ideXlab platform.

  • Low-complexity Graph Sampling With Noise and Signal Reconstruction via Neumann Series
    IEEE Transactions on Signal Processing, 2019
    Co-Authors: Fen Wang, Gene Cheung, Yongchao Wang
    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.

  • fast sampling of graph signals with noise via Neumann Series conversion
    International Conference on Acoustics Speech and Signal Processing, 2019
    Co-Authors: Fen Wang, Gene Cheung, Yongchao Wang
    Abstract:

    Graph sampling with independent noise towards minimum mean square error (MMSE) leads to the known A-optimality criterion, which is computation-intensive to evaluate and NP-hard to optimize. In this paper, we propose a new low-complexity sampling strategy based on Neumann Series that circumvents large matrix inversion and eigen-decomposition. We first prove that a DC-shifted A-optimality criterion is equivalent to an objective computed using the inverse of a sub-matrix of an ideal graph low-pass (LP) filter. The LP filter matrix can be approximated efficiently via fast Graph Fourier Transform (FGFT). Using the shifted A-optimality objective as a proxy, we then propose a fast algorithm to greedily select samples one-by-one based on a matrix inversion lemma with simple matrix updates. We show that the obtained solution has a performance upper bound via super-modularity analysis. Simulation results show that our proposed sampling strategy has lower complexity and outperforms several existing deterministic sampling schemes.

  • ICASSP - Fast Sampling of Graph Signals with Noise via Neumann Series Conversion
    ICASSP 2019 - 2019 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2019
    Co-Authors: Fen Wang, Gene Cheung, Yongchao Wang
    Abstract:

    Graph sampling with independent noise towards minimum mean square error (MMSE) leads to the known A-optimality criterion, which is computation-intensive to evaluate and NP-hard to optimize. In this paper, we propose a new low-complexity sampling strategy based on Neumann Series that circumvents large matrix inversion and eigen-decomposition. We first prove that a DC-shifted A-optimality criterion is equivalent to an objective computed using the inverse of a sub-matrix of an ideal graph low-pass (LP) filter. The LP filter matrix can be approximated efficiently via fast Graph Fourier Transform (FGFT). Using the shifted A-optimality objective as a proxy, we then propose a fast algorithm to greedily select samples one-by-one based on a matrix inversion lemma with simple matrix updates. We show that the obtained solution has a performance upper bound via super-modularity analysis. Simulation results show that our proposed sampling strategy has lower complexity and outperforms several existing deterministic sampling schemes.

Salwa Elramly - One of the best experts on this subject based on the ideXlab platform.

  • Fast Converging Weighted Neumann Series Precoding for Massive MIMO Systems
    IEEE Wireless Communications Letters, 2018
    Co-Authors: Betty Nagy, Maha Elsabrouty, Salwa Elramly
    Abstract:

    Neumann Series (NS) expansion-based precoder in massive multiple input multiple output systems suffers from slow convergence. To solve this problem, this letter proposes a weighted NS expansion precoder. The weights are designed to minimize the error between the exact inverse and the weighted NS inverse. The optimal weights are deduced analytically. Moreover, an approximation of these optimal weights is proposed, based on the properties of large Wishart matrices, which saves the re-computation of these weights. The weighted NS precoding provides near optimal performance at only four weighted expanded NS terms and has lower complexity than recently proposed approximate precoders.