發(fā)布時間：2018-05-24 01:01

  本文選題：l最優(yōu)化 + 反饋神經(jīng)網(wǎng)絡(luò)�。� 參考：《計算機應(yīng)用》2017年09期

【摘要】：針對稀疏信號的重構(gòu)問題,提出了一種基于反饋神經(jīng)網(wǎng)絡(luò)(RNN)的優(yōu)化算法。首先,需要對信號進行稀疏表示,將數(shù)學(xué)模型化為優(yōu)化問題;接著,基于l0范數(shù)是非凸且不可微的函數(shù),并且該優(yōu)化問題是NP難的,因此在測量矩陣A滿足有限等距性質(zhì)(RIP)的前提下,提出等價優(yōu)化問題;最后,通過建立相應(yīng)的Hopfield反饋神經(jīng)網(wǎng)絡(luò)模型來解決等價的優(yōu)化問題,從而實現(xiàn)稀疏信號的重構(gòu)。實驗結(jié)果表明,在不同觀測次數(shù)m下,對比RNN算法和其他三種算法的相對誤差,發(fā)現(xiàn)RNN算法相對誤差小,且需要的觀測數(shù)也少,能夠高效地重構(gòu)稀疏信號。
[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.
【作者單位】： 北京信息科技大學(xué)理學(xué)院;
【基金】：國家自然科學(xué)基金資助項目(61473325)~~
【分類號】：TN911.7;TP183
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本文編號：1927081