IEEE Trans Neural Netw Learn Syst. 2019 Jan;30(1):151-162. doi: 10.1109/TNNLS.2018.2836933. Epub 2018 Jun 5.
This paper deals with sparse signal reconstruction by designing a discrete-time projection neural network. Sparse signal reconstruction can be converted into an L -minimization problem, which can also be changed into the unconstrained basis pursuit denoising problem. To solve the L -minimization problem, an iterative algorithm is proposed based on the discrete-time projection neural network, and the global convergence of the algorithm is analyzed by using Lyapunov method. Experiments on sparse signal reconstruction and several popular face data sets are organized to illustrate the effectiveness and performance of the proposed algorithm. The experimental results show that the proposed algorithm is not only robust to different levels of sparsity and amplitude of signals and the noise pixels but also insensitive to the diverse values of scalar weight. Moreover, the value of the step size of the proposed algorithm is close to 1/2, thus a fast convergence rate is potentially possible. Furthermore, the proposed algorithm achieves better classification performance compared with some other algorithms for face recognition.
本文通过设计离散时间投影神经网络来研究稀疏信号重构问题。稀疏信号重构可以转化为 L -极小化问题，也可以转化为无约束基追踪去噪问题。为了解决 L -极小化问题，提出了一种基于离散时间投影神经网络的迭代算法，并利用 Lyapunov 方法分析了算法的全局收敛性。通过对稀疏信号重构和几个流行的人脸数据集进行实验，验证了所提算法的有效性和性能。实验结果表明，所提算法不仅对不同稀疏度和信号幅度以及噪声像素具有鲁棒性，而且对标量权重的不同值不敏感。此外，所提算法的步长值接近 1/2，因此可能具有较快的收敛速度。此外，与其他一些人脸识别算法相比，所提算法具有更好的分类性能。
