A neural network for minimization based on scaled gradient projection: Application to compressed sensing

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• 作者：Yongwei Liu ^{liuyongwei2012@163.com" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Jianfeng Hu ; ^{lakerhjf@163.com" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Neural network ; Scaled gradient projection ; ℓ_1&minus ; ℓ_2ℓ1&minus ; ℓ2 minimization ; Compressed sensing
• 刊名：Neurocomputing
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：173
• 期：part_P3
• 页码：988-993
• 全文大小：903 K

文摘

Since compressed sensing was introduced in 2006, ℓ₁−ℓ₂${\ell }_1-{\ell }_2$ minimization admits a large number of applications in signal processing, statistical inference, magnetic resonance imaging (MRI), computed tomography (CT), etc. In this paper, we present a neural network for ℓ₁−ℓ₂${\ell }_1-{\ell }_2$ minimization based on scaled gradient projection. We prove that it is stable in the sense of Lyapunov and converges to an optimal solution of the ℓ₁−ℓ₂${\ell }_1-{\ell }_2$ minimization. We show that the proposed neural network is feasible and efficient for compressed sensing via simulation examples.