矩阵填充及其在信号处理中的应用

Matrix Completion and Its Application in Signal Processing

本文首先阐述了矩阵填充的应用背景,给出了矩阵填充的数学模型,详细分析了矩阵填充中的低秩特性和非相干特性,重点介绍了矩阵填充三种典型的重构算法:SVT(Singular Value Thresholding)算法、ADMiRA(Atomic Decomposition for Minimum Rank Approximation)算法和SVP(Singular Value Projection)算法,文中的仿真实验对这三种算法的重构性能进行了比较;文章随后分析了矩阵填充和压缩感知的联系;最后介绍了矩阵填充在协同过滤、系统识别、传感器网络、图像处理、稀疏信道估计、频谱感知以及多媒体编码和通信等方面的的应用。

This paper describes the background of matrix completion firstly,points out the mathematics model of matrix completion,analyzes the low rank property and the incoherence property in matrix completion.Malnly introduces three re-construction algorithm commonly used in matrix completion：SVT（Singular Value Thresholding）、ADMiRA（Atomic Decom-position for Minimum Rank Approximation）and SVP（Singular Value Projection）,compares their reconstruction perform-ance in this paper.Secondly,we analyze the connection between matrix completion and compressed sensing.Finally we in-troduce the application of matrix completion in collaborative filtering,system identification,sensor network,image process-ing,sparse channel estimation,spectrum sensing and multimedia coding and communication.