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    Power-Constrained Sparse Gaussian Linear Dimensionality Reduction over Noisy Channels


    Shirazinia, Amirpasha and Dey, Subhrakanti (2015) Power-Constrained Sparse Gaussian Linear Dimensionality Reduction over Noisy Channels. IEEE Transactions on Signal Processing, 63 (21). pp. 5837-5852. ISSN 1053-587X

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    Abstract

    In this paper, we investigate power-constrained sensing matrix design in a sparse Gaussian linear dimensionality reduction framework. Our study is carried out in a single–terminal setup as well as in a multi–terminal setup consisting of orthogonal or coherent multiple access channels (MAC). We adopt the mean square error (MSE) performance criterion for sparse source reconstruction in a system where source-to-sensor channel(s) and sensor-to-decoder communication channel(s) are noisy. Our proposed sensing matrix design procedure relies upon minimizing a lower-bound on the MSE in single– and multiple–terminal setups. We propose a three-stage sensing matrix optimization scheme that combines semi-definite relaxation (SDR) programming, a low-rank approximation problem and power-rescaling. Under certain conditions, we derive closedform solutions to the proposed optimization procedure. Through numerical experiments, by applying practical sparse reconstruction algorithms, we show the superiority of the proposed scheme by comparing it with other relevant methods. This performance improvement is achieved at the price of higher computational complexity. Hence, in order to address the complexity burden, we present an equivalent stochastic optimization method to the problem of interest that can be solved approximately, while still providing a superior performance over the popular methods.

    Item Type: Article
    Keywords: Compressed sensing; convex optimization; low rank; MAC; MSE; sensing matrix; sparse gaussian;
    Academic Unit: Faculty of Science and Engineering > Electronic Engineering
    Item ID: 12702
    Identification Number: https://doi.org/10.1109/TSP.2015.2455521
    Depositing User: Subhrakanti Dey
    Date Deposited: 06 Apr 2020 11:07
    Journal or Publication Title: IEEE Transactions on Signal Processing
    Publisher: Institute of Electrical and Electronics Engineers
    Refereed: Yes
    URI:

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