压缩传感中CS矩阵的构造理论与信号重构的快速算法

项目名称： 压缩传感中CS矩阵的构造理论与信号重构的快速算法

项目编号： No.11271117

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： 廖安平

作者单位： 湖南大学

项目金额： 70万元

中文摘要： 近年来，在信号处理领域中出现了以压缩传感为代表的新兴采样方式，这种方式以信号的稀疏性为基础，突破了香农-奈奎斯特采样定理的限制，使欠采样成为了可能，大大地节约了采样时间和传感器资源。然而,受欠采样自身性质的影响，压缩传感中信号恢复的过程与传统采样方法相比更为复杂，导致这一优越的采样方法距实际应用尚有一定的距离。基于这一现状，本项目拟从压缩传感中感知矩阵（CS矩阵）的构造出发，从理论上给出易于验证的CS矩阵限制条件，进而为图像、声音等几类典型的信号构造出易于重构的CS矩阵，并将这些矩阵与这些信号自身的性质相结合，设计出信号重构的快速算法。此外，对于多维信号的压缩传感，本项目拟引入"CS张量"，给出一些可用CS张量采样的信号类，进而研究压缩传感中多维信号的重构算法。

中文关键词： 压缩感知；稀疏信号；CS矩阵；正交匹配追踪算法；多重测量

英文摘要： In recent years, a novel sampling method delegated by Compressed Sensing has emerged in signal processing region.This method was based on the sparse property of some classes of signals and broke the restriction that was introduced by Shanon and Nyquist,so that undersampling was enabled and as a result, it saves a lot of time and sensor resources. However, with the reflect caused by undersampling, the signal reconstruction procedure is more complex than traditional methods, which created a big gap between the premium sampling method and pratical application.To deal with this reality, our project plans to begin with the structure of CS-matrix, brings some restrict conditions for CS-matrices that will be verified easily, and constructs some CS-matrices for some classical signals such as digital image and sound,and by combining the properties of these matrices with that of of such signals as a whole, designs some fast algorithms for the construction of these signals. In addition, to deal with Compressed Sensing for high dimensional signals, our project tends to introduce a concept names "CS-tensor"，defines some classes of signals that could be sampled by CS-tensor and gets a deeper research for signal construction of multi-dimensional signals' Compressed Sensing.

英文关键词： compressed sensing；sparse signal；CS matrices；orthogonal matching pursuing；multiple measurement vector