信号稀疏表示与重构的神经网络算法研究

项目名称： 信号稀疏表示与重构的神经网络算法研究

项目编号： No.61473325

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 其他

项目作者： 李国成

作者单位： 北京信息科技大学

项目金额： 59万元

中文摘要： 本项目采用神经网络算法解决压缩感知理论中信号的稀疏表示与重构问题，针对信号的稀疏性特征和重构要求，在泛函空间和矩阵理论的框架下合理地构造出包含稀疏偏差项与稀疏诱导惩罚项的目标函数，理论上证明其与原问题的等价性。基于目标函数的性质，设计出快速解决稀疏表示与精确重构的神经网络算法，该网络具有良好的稳定性，可以快速收敛到问题的精确解，可弥补已有算法无法精确恢复信号、复杂度高、不能实时执行的缺陷。针对具体的视频时间序列信号，利用所设计的神经网路模型模拟电路实现，对所得到的时间序列视频信号的平滑性、稳定性、清晰度等性能进行评价，并与已有的算法进行比较。本项目为解决压缩感知理论中信号的实时合理的稀疏表示与精确重构问题提出了高效解决方法，可保证快速实时实现信号的压缩感知处理，为使用大规模集成电路（VLSI）重构模拟芯片来实现信号的稀疏表示和重构奠定了理论基础。

中文关键词： 稀疏表示；稀疏重构；压缩感知；神经网络；收敛性

英文摘要： The approach of this project is to solve sparse presentation and reconstruction problems in compressed sensing theory by neural network algorithm.In light of the sparse characteristics and the requirements on reconstruction,an object function with sparse deviation term and penalty term inducing sparse is properly constructed under functional space and matrix theory. The object function is proven to be equivalent to the original problem in theory.Based on the properties of the object function, neural network algorithm which can make sparse presentation quickly and reconstruction exactly is designed.The network has good stability and can converge to the precise solution of the problem quickly.This approach makes up the shortages of the existing algorithms which are highly complicated,unable to recover the signal exactly and unable to execute at real time.An Analog circuit is designed to realize the neural network model to process video time-sequence signal.The smoothness, stability and definition of the output signal are evaluated,comparison with existing algorithms is conducted as well. This project provides an efficient solution for proper real time sparse presentation and exact reconstruction of signals in compressed sensing theory.It ensures real time quick compressed sensing processing of signals and lays a theory foundation for using very-large-scale integration (VLSI) reconstruction analog chips to realize signal sparse presentation and reconstruction.

英文关键词： sparse representation;sparse reconstruction;compressed sensing;neural networks;convergence