基于反馈神经网络的稀疏信号恢复的优化算法

发布时间：2018-05-24 01:01

  本文选题：l最优化 + 反馈神经网络　； 参考：《计算机应用》2017年09期

【摘要】：针对稀疏信号的重构问题,提出了一种基于反馈神经网络(RNN)的优化算法。首先,需要对信号进行稀疏表示,将数学模型化为优化问题;接着,基于l0范数是非凸且不可微的函数,并且该优化问题是NP难的,因此在测量矩阵A满足有限等距性质(RIP)的前提下,提出等价优化问题;最后,通过建立相应的Hopfield反馈神经网络模型来解决等价的优化问题,从而实现稀疏信号的重构。实验结果表明,在不同观测次数m下,对比RNN算法和其他三种算法的相对误差,发现RNN算法相对误差小,且需要的观测数也少,能够高效地重构稀疏信号。
[Abstract]:To solve the problem of sparse signal reconstruction, an optimization algorithm based on feedback neural network (RNNN) is proposed. First, the signal needs to be represented sparsely, and the mathematical model is transformed into an optimization problem. Then, based on the non-convex and non-differentiable function of l0 norm, the optimization problem is NP-hard. So on the premise that the measurement matrix A satisfies the finite isometric property, the equivalent optimization problem is proposed. Finally, the corresponding Hopfield feedback neural network model is established to solve the equivalent optimization problem, and the sparse signal reconstruction is realized. The experimental results show that compared with the other three algorithms, the relative error of RNN algorithm is small and the number of observations needed by RNN algorithm is small, so the sparse signal can be reconstructed efficiently.
【作者单位】： 北京信息科技大学理学院;
【基金】：国家自然科学基金资助项目(61473325)~~
【分类号】：TN911.7;TP183
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本文编号：1927081