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Author: Li, Lixiang ×

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    Overview of compressed sensing: Sensing model, reconstruction algorithm, and its applications
    (Basel : MDPI, 2020) Li, Lixiang; Fang, Yuan; Liu, Liwei; Peng, Haipeng; Kurths, Jürgen; Yang, Yixian
    With the development of intelligent networks such as the Internet of Things, network scales are becoming increasingly larger, and network environments increasingly complex, which brings a great challenge to network communication. The issues of energy-saving, transmission efficiency, and security were gradually highlighted. Compressed sensing (CS) helps to simultaneously solve those three problems in the communication of intelligent networks. In CS, fewer samples are required to reconstruct sparse or compressible signals, which breaks the restrict condition of a traditional Nyquist-Shannon sampling theorem. Here, we give an overview of recent CS studies, along the issues of sensing models, reconstruction algorithms, and their applications. First, we introduce several common sensing methods for CS, like sparse dictionary sensing, block-compressed sensing, and chaotic compressed sensing. We also present several state-of-the-art reconstruction algorithms of CS, including the convex optimization, greedy, and Bayesian algorithms. Lastly, we offer recommendation for broad CS applications, such as data compression, image processing, cryptography, and the reconstruction of complex networks. We discuss works related to CS technology and some CS essentials. © 2020 by the authors.
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    The stability of memristive multidirectional associative memory neural networks with time-varying delays in the leakage terms via sampled-data control
    (San Francisco, California, US : PLOS, 2018) Wang, Weiping; Yu, Xin; Luo, Xiong; Wang, Long; Li, Lixiang; Kurths, Jürgen; Zhao, Wenbing; Xiao, Jiuhong
    In this paper, we propose a new model of memristive multidirectional associative memory neural networks, which concludes the time-varying delays in leakage terms via sampled-data control. We use the input delay method to turn the sampling system into a continuous time-delaying system. Then we analyze the exponential stability and asymptotic stability of the equilibrium points for this model. By constructing a suitable Lyapunov function, using the Lyapunov stability theorem and some inequality techniques, some sufficient criteria for ensuring the stability of equilibrium points are obtained. Finally, numerical examples are given to demonstrate the effectiveness of our results.