固定时间梯度流在l1-l2范数中的稀疏重构

压缩感知（compressed sensing，CS）是一种全新的信号采样技术，对于稀疏信号，它能够以远小于传统的Nyquist采样定理的采样点来重构信号。在压缩感知中， 采用动态连续系统，对l₁-l₂范数的稀疏信号重构问题进行了研究。提出了一种基于固定时间梯度流的稀疏信号重构算法，证明了该算法在Lyapunov意义上的稳定性并且收敛于问题的最优解。最后通过与现有的投影神经网络算法的对比，体现了该算法的可行性以及在收敛速度上的优势.

Sparse Reconstruction of Fixed-Time Gradient Flow in the l1-l2 Norm

The compressed sensing (CS) is a new signal sampling technology, which can reconstruct signals at sampling points far smaller than those in the traditional Nyquist sampling theorem for sparse signals. For the compressed sensing, a dynamic continuous system was used to study the sparse signal reconstruction of the l₁l-l₂ norm. A sparse signal reconstruction algorithm based on the fixed time gradient flow was proposed, and was proved to be stable in the sense of Lyapunov and to converge to the optimal solution of the problem. Finally, the feasibility and advantages in the convergence speed of this algorithm were demonstrated through comparison between the proposed algorithm and existing projection neural network algorithms.