感知压缩理论中信号重构算法
毕业论文关键词 压缩感知 信号重构 匹配追踪 凸优化算法
Title Perception in compression theory of signal
reconstruction algorithm
Abstract
Approximate sparse signal has become a basic tool for signal processing,
separation from the source to the extensive application in the process of
signal acquisition.Feasible scheme of growing, especially now is
continuously increasing capacity to deal with problems, lead to in
computational strategies lead to new challenges and development of fast
and efficient algorithm is particularly important.Recently, the fast
algorithm was developed to solve the problem of convex optimization, are
often used to approximate the sparse approximation problem;Algorithm,
however, show that in certain cases, the greedy strategy, such as
orthogonal matching pursuit algorithm, has better performance than convex
optimization method.In this article, we are interested in the greedy
method, the most important thing is matching pursuit (MP), orthogonal
matching pursuit (OMP), and the orthogonal least squares (OLS).In view of
the existing two kinds of reconstruction algorithms were introduced: one
kind is a series of greedy algorithm for minimum norm, one kind is in view
of the minimum norm of the convex optimization algorithm.
Keywords Compressed sensing signal reconstruction matching pursuit
convex optimization algorithm 目 次
1 引言 1
2 压缩感知理论 1
2.1 传统感知和压缩感知 1
2.2 压缩感知理论 4
3 信号重构 6
3.1 信号重构简述 6
3.2匹配追踪类重构算法 7
3.3 凸优化算法 11
结论 13
致谢 14
参考文献15
1 引言
在现实生活中，采样联系着模拟信源和数字信息。人们对信息的巨量需求提高了
了信号采样、传输和存储的巨大压力成本。为了降低这种压力成本，人们常采用压缩
的方式以较少传输、存储的数据量，抛弃大量的非关键的数据。高速采样再压缩的过
程浪费了大量的时间、空间，于是引出这样一个问题：能否利用其它变换空间描述信
号，建立新的信号描述和处理的理论框架，使得在保证信息不损失的情况下，用远低
于当下的信号采集量，同时又可以完全恢复或极大的恢复信号？于是， “稀疏性”一
词近期频频出现在多个学科的各个研究领域中。稀疏信号是指信号的大部分元素为 0
或者是大部分元素接近0。因此，这种信号是可以被压缩的，进而可以节约储存空间，
需求更少的传输通道和传输时间。最近3 0 年左右，“稀疏性”已经在信息的分析、传
输和处理领域崭露头角，凸显其优越性。尤其在最近，新兴的研究方向”压缩感知”
利用信号、 信息的稀疏性， 提高了信号的采集以及处理能力， 缓解了海量数据的采样、
存储、传输和分析越的负担。在这些工作中，稀疏优化起到了核心的作用,得到了大
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