测量值相关的稀疏信号可重构条件研究

项目名称： 测量值相关的稀疏信号可重构条件研究

项目编号： No.11271297

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 李海洋

作者单位： 西安交通大学

项目金额： 60万元

中文摘要： 稀疏信号重构是压缩感知理论中的核心问题。现有的稀疏信号可重构的条件研究主要是基于测量矩阵的性质（包括矩阵的Spark、相干性和Babel 函数，以及矩阵的k-约束等距常数等），而没有考虑到测量值的作用，因此得到的稀疏信号可重构条件过于保守，过于刚性；现有的重构算法也大多是基于优化1-范数而发展起来的，因而存在数据的大量冗余难以去除、稀疏系数尺度的位置难以区分等不足。所以，建立与测量值相关的稀疏信号可重构的条件和发展新的重构算法具有重要的理论意义和应用价值。本项目拟在研究测量值与测量矩阵组成的增广矩阵的特性以及向量的最小线性表示理论的基础上，对与测量值相关的稀疏信号可重构的本质特征和0-范数优化问题的新重构算法进行深入研究，旨在为稀疏信号重构问题的研究探索出一种新的理论和方法。

中文关键词： 压缩感知；0-范数优化问题；重构算法；稀疏凸优化；测量矩阵的预处理

英文摘要： The core issue in compressive sensing is sparse signal reconstruction. The present research on the reconstructed conditions of sparse signals are mainly based on the properties of the measured matrix, including the spark, mutual-coherence, Babel function and the k-restricted isometry constants of matrix, but it doesn't consider the effects of measured value. As a result, the reconstruction conditions of sparse signals which it got are too conservative and too rigid. Moreover, the present reconstruction algorithms mostly developed from an optimization problem using 1-norm regularization, and hence there exist the quantities of redundant data which is hard omit and the position of the scale coefficient of sparse is difficult to distinguish. Therefore, it is important and meaningful both in theory and application to bulid the reconstruction codtions of sparse sigals which is related to measured value and develop the new reconstruction algorithm. The project aims to do a in-depth study into the essential characteristics of spare signal reconstruction related to measured value and the new reconstruction algorithm for 0-norm optimization problems, based on investigating the characteristics of augmented matrix made up of measured value and measured matrix and the minimum linear representation theory of vector, and e

英文关键词： Compressed Sensing；l0-norm Optimization Problem；Reconstruction Algorithm；Sparse Convex Optimization；Preconditioning of the Measurement Matrices